Solution Manual for Economics, 2nd Edition
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Microeconomics
Second Edition
Daron Acemoglu
David Laibson
John List
Solutions Manual
Scott Ogawa
Northwestern University
Second Edition
Daron Acemoglu
David Laibson
John List
Solutions Manual
Scott Ogawa
Northwestern University
Chapter 1
The Principles and Practice of Economics
Questions
1. Why do we have to pay a price for most of the goods we consume?
Answer: The inputs we use to produce most goods and services (for example, capital and labor) are
scarce. Therefore almost all goods and services are scarce compared to the quantity that consumers
want to consume. In other words, at a price of zero the demand for most goods is higher than the
available supply; our wants are unlimited but our resources are not. Prices act as a rationing
mechanism to prevent the over-consumption of such scarce goods, making them available in the
quantity such that the supply of these goods matches the demand.
2. Many people believe that the study of economics is focused on money and financial markets.
Based on your reading of the chapter, how would you define economics?
Answer: Economics is the study of how agents (for example, households and firms) choose to allocate
scarce resources and how these choices affect society. Although it is true that economics studies
money and the financial markets, the study of economics is really focused on human behavior and
choices. Given that we have limited resources, we need to choose between various options. Economic
analysis is used to understand people’s choices in order to describe what people do and recommend
what people ought to do.
3. Examine the following statements and determine if they are normative or positive in nature.
Explain your answer.
a. Car sales in Europe rose 9.3 percent from 2014 to 2015.
b. The U.S. government should increase carbon taxes to control emissions that cause global
warming.
Answer:
a. This is an objective statement about the rate of growth in the European automotive industry.
Positive economics is analysis that generates objective descriptions or predictions about the
world that can be verified with data. Since data can be used here to verify the rate of growth,
this is a positive statement.
b. The statement that the government should increase carbon taxes to control emissions is
normative since it states what the government ought to do. Normative economics advises
individuals and society on their decisions and is almost always dependent on subjective
judgments.
4. How does microeconomics differ from macroeconomics? Would the supply of iPhones in the
United States be studied under microeconomics or macroeconomics? What about the growth rate
of total economic output in the national economy?
Answer: Microeconomics is the study of how individuals, households, firms, and governments make
choices, and how those choices affect prices, the allocation of resources, and the well-being of other
The Principles and Practice of Economics
Questions
1. Why do we have to pay a price for most of the goods we consume?
Answer: The inputs we use to produce most goods and services (for example, capital and labor) are
scarce. Therefore almost all goods and services are scarce compared to the quantity that consumers
want to consume. In other words, at a price of zero the demand for most goods is higher than the
available supply; our wants are unlimited but our resources are not. Prices act as a rationing
mechanism to prevent the over-consumption of such scarce goods, making them available in the
quantity such that the supply of these goods matches the demand.
2. Many people believe that the study of economics is focused on money and financial markets.
Based on your reading of the chapter, how would you define economics?
Answer: Economics is the study of how agents (for example, households and firms) choose to allocate
scarce resources and how these choices affect society. Although it is true that economics studies
money and the financial markets, the study of economics is really focused on human behavior and
choices. Given that we have limited resources, we need to choose between various options. Economic
analysis is used to understand people’s choices in order to describe what people do and recommend
what people ought to do.
3. Examine the following statements and determine if they are normative or positive in nature.
Explain your answer.
a. Car sales in Europe rose 9.3 percent from 2014 to 2015.
b. The U.S. government should increase carbon taxes to control emissions that cause global
warming.
Answer:
a. This is an objective statement about the rate of growth in the European automotive industry.
Positive economics is analysis that generates objective descriptions or predictions about the
world that can be verified with data. Since data can be used here to verify the rate of growth,
this is a positive statement.
b. The statement that the government should increase carbon taxes to control emissions is
normative since it states what the government ought to do. Normative economics advises
individuals and society on their decisions and is almost always dependent on subjective
judgments.
4. How does microeconomics differ from macroeconomics? Would the supply of iPhones in the
United States be studied under microeconomics or macroeconomics? What about the growth rate
of total economic output in the national economy?
Answer: Microeconomics is the study of how individuals, households, firms, and governments make
choices, and how those choices affect prices, the allocation of resources, and the well-being of other
Chapter 1
The Principles and Practice of Economics
Questions
1. Why do we have to pay a price for most of the goods we consume?
Answer: The inputs we use to produce most goods and services (for example, capital and labor) are
scarce. Therefore almost all goods and services are scarce compared to the quantity that consumers
want to consume. In other words, at a price of zero the demand for most goods is higher than the
available supply; our wants are unlimited but our resources are not. Prices act as a rationing
mechanism to prevent the over-consumption of such scarce goods, making them available in the
quantity such that the supply of these goods matches the demand.
2. Many people believe that the study of economics is focused on money and financial markets.
Based on your reading of the chapter, how would you define economics?
Answer: Economics is the study of how agents (for example, households and firms) choose to allocate
scarce resources and how these choices affect society. Although it is true that economics studies
money and the financial markets, the study of economics is really focused on human behavior and
choices. Given that we have limited resources, we need to choose between various options. Economic
analysis is used to understand people’s choices in order to describe what people do and recommend
what people ought to do.
3. Examine the following statements and determine if they are normative or positive in nature.
Explain your answer.
a. Car sales in Europe rose 9.3 percent from 2014 to 2015.
b. The U.S. government should increase carbon taxes to control emissions that cause global
warming.
Answer:
a. This is an objective statement about the rate of growth in the European automotive industry.
Positive economics is analysis that generates objective descriptions or predictions about the
world that can be verified with data. Since data can be used here to verify the rate of growth,
this is a positive statement.
b. The statement that the government should increase carbon taxes to control emissions is
normative since it states what the government ought to do. Normative economics advises
individuals and society on their decisions and is almost always dependent on subjective
judgments.
4. How does microeconomics differ from macroeconomics? Would the supply of iPhones in the
United States be studied under microeconomics or macroeconomics? What about the growth rate
of total economic output in the national economy?
Answer: Microeconomics is the study of how individuals, households, firms, and governments make
choices, and how those choices affect prices, the allocation of resources, and the well-being of other
The Principles and Practice of Economics
Questions
1. Why do we have to pay a price for most of the goods we consume?
Answer: The inputs we use to produce most goods and services (for example, capital and labor) are
scarce. Therefore almost all goods and services are scarce compared to the quantity that consumers
want to consume. In other words, at a price of zero the demand for most goods is higher than the
available supply; our wants are unlimited but our resources are not. Prices act as a rationing
mechanism to prevent the over-consumption of such scarce goods, making them available in the
quantity such that the supply of these goods matches the demand.
2. Many people believe that the study of economics is focused on money and financial markets.
Based on your reading of the chapter, how would you define economics?
Answer: Economics is the study of how agents (for example, households and firms) choose to allocate
scarce resources and how these choices affect society. Although it is true that economics studies
money and the financial markets, the study of economics is really focused on human behavior and
choices. Given that we have limited resources, we need to choose between various options. Economic
analysis is used to understand people’s choices in order to describe what people do and recommend
what people ought to do.
3. Examine the following statements and determine if they are normative or positive in nature.
Explain your answer.
a. Car sales in Europe rose 9.3 percent from 2014 to 2015.
b. The U.S. government should increase carbon taxes to control emissions that cause global
warming.
Answer:
a. This is an objective statement about the rate of growth in the European automotive industry.
Positive economics is analysis that generates objective descriptions or predictions about the
world that can be verified with data. Since data can be used here to verify the rate of growth,
this is a positive statement.
b. The statement that the government should increase carbon taxes to control emissions is
normative since it states what the government ought to do. Normative economics advises
individuals and society on their decisions and is almost always dependent on subjective
judgments.
4. How does microeconomics differ from macroeconomics? Would the supply of iPhones in the
United States be studied under microeconomics or macroeconomics? What about the growth rate
of total economic output in the national economy?
Answer: Microeconomics is the study of how individuals, households, firms, and governments make
choices, and how those choices affect prices, the allocation of resources, and the well-being of other
Chapter 1 | The Principles and Practice of Economics 2
agents. Macroeconomics is the study of the economy as a whole. Macroeconomists study factors that
affect overall – in other words, aggregate – economic performance.
The supply of iPhones refers to the supply of a good by an individual firm, Apple. The iPhone market
will be studied under microeconomics. Microeconomics studies how individuals, households, firms
and governments make choices, and how those choices affect prices and the allocation of resources.
The growth rate of total economic output, on the other hand, refers to the aggregate American
economy, and is therefore studied under macroeconomics.
5. What does a budget constraint represent? How do budget constraints explain the trade-offs that
consumers face?
Answer: A budget constraint is an equation representing the goods or activities that a consumer can
choose given her limited budget. Tradeoffs arise when some benefits must be given up in order to
gain others. In other words, a trade-off occurs when you give one thing up to get something else.
Since a budget constraint shows the set of things that you can choose to do or buy with a fixed
amount of money, it also shows that if you choose to buy more of one good, you will have to buy less
of another. Therefore, a budget constraint equation implies that a consumer faces a tradeoff.
6. This chapter introduces the idea of opportunity cost.
a. What is meant by opportunity cost?
b. What is the opportunity cost of taking a year after graduating from high school and
backpacking across Europe? Are people who do so being irrational?
Answer:
a. Opportunity cost is the best alternative use of a resource. The opportunity cost of a particular
choice is measured in terms of the benefit foregone from the next best alternative. To
facilitate comparison, the benefits and costs of various choices are translated into monetary
units like dollars.
b. The opportunity cost of backpacking across Europe, for a particular person, is the cost of
anything else that could have been done in that year. The backpacker could have attended
college or started working. These costs are the opportunity costs of the gap year. This,
however, does not mean that backpackers are irrational, because the benefits may exceed the
cost. Every action has an opportunity cost. The choices that people make are optimal based
on their perceived costs and benefits.
7. The costs of many environmental regulations can be calculated in dollars—for instance, the cost
of “scrubbers” that reduce the amount of air pollution emitted by a coal factory. The benefits of
environmental regulations often are most directly expressed in terms of lives saved (reduced
mortality) or decreases in the incidence of a particular disease (reduced morbidity). What does
this imply about the cost-benefit analysis of environmental regulations? There is an old saying
“You can’t put a price on a human life.” Do you agree or disagree? Explain.
Answer: Cost-benefit analysis can be used when there is a common unit, such as dollars. This method
is less straightforward if there are two different units of measurement, such as dollars and lives.
However, if a direct link can be drawn between dollars spent and lives saved then cost-benefit
analysis becomes feasible. When an environmental regulator places a value of 3 million dollars on a
human life (for example), they are claiming that if 3 million dollars is not spent in one area, then it
can instead be spent in another area where 3 million dollars is expected to save one life, on average.
While some people may find this practice controversial, it does provide the most practical way to
maximize the number of lives saved, given limited financial resources.
agents. Macroeconomics is the study of the economy as a whole. Macroeconomists study factors that
affect overall – in other words, aggregate – economic performance.
The supply of iPhones refers to the supply of a good by an individual firm, Apple. The iPhone market
will be studied under microeconomics. Microeconomics studies how individuals, households, firms
and governments make choices, and how those choices affect prices and the allocation of resources.
The growth rate of total economic output, on the other hand, refers to the aggregate American
economy, and is therefore studied under macroeconomics.
5. What does a budget constraint represent? How do budget constraints explain the trade-offs that
consumers face?
Answer: A budget constraint is an equation representing the goods or activities that a consumer can
choose given her limited budget. Tradeoffs arise when some benefits must be given up in order to
gain others. In other words, a trade-off occurs when you give one thing up to get something else.
Since a budget constraint shows the set of things that you can choose to do or buy with a fixed
amount of money, it also shows that if you choose to buy more of one good, you will have to buy less
of another. Therefore, a budget constraint equation implies that a consumer faces a tradeoff.
6. This chapter introduces the idea of opportunity cost.
a. What is meant by opportunity cost?
b. What is the opportunity cost of taking a year after graduating from high school and
backpacking across Europe? Are people who do so being irrational?
Answer:
a. Opportunity cost is the best alternative use of a resource. The opportunity cost of a particular
choice is measured in terms of the benefit foregone from the next best alternative. To
facilitate comparison, the benefits and costs of various choices are translated into monetary
units like dollars.
b. The opportunity cost of backpacking across Europe, for a particular person, is the cost of
anything else that could have been done in that year. The backpacker could have attended
college or started working. These costs are the opportunity costs of the gap year. This,
however, does not mean that backpackers are irrational, because the benefits may exceed the
cost. Every action has an opportunity cost. The choices that people make are optimal based
on their perceived costs and benefits.
7. The costs of many environmental regulations can be calculated in dollars—for instance, the cost
of “scrubbers” that reduce the amount of air pollution emitted by a coal factory. The benefits of
environmental regulations often are most directly expressed in terms of lives saved (reduced
mortality) or decreases in the incidence of a particular disease (reduced morbidity). What does
this imply about the cost-benefit analysis of environmental regulations? There is an old saying
“You can’t put a price on a human life.” Do you agree or disagree? Explain.
Answer: Cost-benefit analysis can be used when there is a common unit, such as dollars. This method
is less straightforward if there are two different units of measurement, such as dollars and lives.
However, if a direct link can be drawn between dollars spent and lives saved then cost-benefit
analysis becomes feasible. When an environmental regulator places a value of 3 million dollars on a
human life (for example), they are claiming that if 3 million dollars is not spent in one area, then it
can instead be spent in another area where 3 million dollars is expected to save one life, on average.
While some people may find this practice controversial, it does provide the most practical way to
maximize the number of lives saved, given limited financial resources.
Chapter 1 | The Principles and Practice of Economics 3
8. Suppose the market price of corn is $5.50 per bushel. What are the three conditions that will need
to be satisfied for the corn market to be in equilibrium at this price?
Answer: For the market to be in equilibrium, three conditions will need to be satisfied.
● At the price of $5.50 per bushel, the amount of corn produced by sellers should be equal to
the amount of corn purchased by buyers in the market.
● Farmers have chosen the optimal quantity of corn to produce given the price of $5.50 per
bushel.
● Consumers have chosen the optimal quantity of corn to buy given the price of $5.50 per
bushel.
9. Economists are often concerned with the free-rider problem.
a. What is meant by free riding? Explain with an example.
b. Are public parks subject to the free-rider problem? What about keeping city streets clean?
Explain your answer.
Answer:
a. A free rider is a person who receives the benefit of a good but avoids paying for it. People
tend to pursue their own private interests and usually don’t contribute voluntarily to the
public interest. For example, watching a pirated copy of a movie is cheaper than buying one.
Those who watch the pirated version are free riders because there are others who buy the
movie or pay for movie tickets. If everyone watched pirated copies, making movies would
not be profitable and the industry would not function.
b. Cleaning of city streets may be subject to free riding. Suppose the streets are cleaned every
day at a fixed cost. This cost is borne by those who pay taxes to the city government.
However, they cannot prevent others who do not pay taxes from using the clean streets. This
leads to the free rider problem. However, not all free riding is necessarily problematic. For a
park that already exists, it is good when many people enjoy its benefits, especially when there
are no real costs associated with usage. The park example demonstrates that free riding is not
a problem per se. Rather, it may lead to the underproduction of public goods -- but once a
particular public good exists people should use it as much as possible, so long as they do not
get in other people’s way.
10. Explain the concept of causation with the help of a simple real-life example.
Answer: Causation is a relationship between two events or states, such that one brings about a change
in the other. In short, it explains the cause and effect relationship between two variables or events. For
example, people who go to college learn skills that are valuable to prospective employers. So a
college degree causes someone’s wages to rise.
11. Identify the cause and the effect in the following examples:
a. A rise in the worldwide price of peaches and a drought in California.
b. A surge in cocoa prices and a pest attack on the cocoa crop that year.
Answer:
a. A drought in California causes a decrease in supply of peaches, and thus a rise in price.
b. The pest attack is likely to have reduced the cocoa crop, leading to a rise in prices.
8. Suppose the market price of corn is $5.50 per bushel. What are the three conditions that will need
to be satisfied for the corn market to be in equilibrium at this price?
Answer: For the market to be in equilibrium, three conditions will need to be satisfied.
● At the price of $5.50 per bushel, the amount of corn produced by sellers should be equal to
the amount of corn purchased by buyers in the market.
● Farmers have chosen the optimal quantity of corn to produce given the price of $5.50 per
bushel.
● Consumers have chosen the optimal quantity of corn to buy given the price of $5.50 per
bushel.
9. Economists are often concerned with the free-rider problem.
a. What is meant by free riding? Explain with an example.
b. Are public parks subject to the free-rider problem? What about keeping city streets clean?
Explain your answer.
Answer:
a. A free rider is a person who receives the benefit of a good but avoids paying for it. People
tend to pursue their own private interests and usually don’t contribute voluntarily to the
public interest. For example, watching a pirated copy of a movie is cheaper than buying one.
Those who watch the pirated version are free riders because there are others who buy the
movie or pay for movie tickets. If everyone watched pirated copies, making movies would
not be profitable and the industry would not function.
b. Cleaning of city streets may be subject to free riding. Suppose the streets are cleaned every
day at a fixed cost. This cost is borne by those who pay taxes to the city government.
However, they cannot prevent others who do not pay taxes from using the clean streets. This
leads to the free rider problem. However, not all free riding is necessarily problematic. For a
park that already exists, it is good when many people enjoy its benefits, especially when there
are no real costs associated with usage. The park example demonstrates that free riding is not
a problem per se. Rather, it may lead to the underproduction of public goods -- but once a
particular public good exists people should use it as much as possible, so long as they do not
get in other people’s way.
10. Explain the concept of causation with the help of a simple real-life example.
Answer: Causation is a relationship between two events or states, such that one brings about a change
in the other. In short, it explains the cause and effect relationship between two variables or events. For
example, people who go to college learn skills that are valuable to prospective employers. So a
college degree causes someone’s wages to rise.
11. Identify the cause and the effect in the following examples:
a. A rise in the worldwide price of peaches and a drought in California.
b. A surge in cocoa prices and a pest attack on the cocoa crop that year.
Answer:
a. A drought in California causes a decrease in supply of peaches, and thus a rise in price.
b. The pest attack is likely to have reduced the cocoa crop, leading to a rise in prices.
Chapter 1 | The Principles and Practice of Economics 4
Problems
1. You have already purchased (non-refundable and unsellable) tickets to a concert on Friday night. A
friend also invites you to her birthday party on Friday. While you like your friend, you politely
decline because you really want to go to the concert.
a. You learn that your friend is serving flank steak at her party, all-you-can eat and at no charge.
Flank steak is your favorite food. Should this affect your decision to go to the concert? Explain by
using the term “opportunity cost.”
b. Suppose instead that you notice that the non-refundable concert ticket (that you already
purchased) cost you $10; previously you had mistakenly believed the price was $100. Should
learning this information affect your decision to go to the concert?
Answer:
a. This should affect your decision, or at least make you reconsider. The explicit cost of the concert
has not changed, nor the benefit of the concert itself. However, the opportunity cost of missing
the party is now higher than you previously thought.
b. This should not affect your decision. Whether you paid ($10 or $100) in the past is irrelevant to
the costs and benefits that you can affect by going (or not going) to the concert.
2. You are thinking about buying a house. You find one you like that costs $200,000. You learn that
your bank will give you a mortgage for $160,000 and that you would have to use all of your savings
to make the down payment of $40,000. You calculate that the mortgage payments, property taxes,
insurance, maintenance, and utilities would total $950 per month. Is $950 the cost of owning the
house? What important factor(s) have you left out of your calculation of the cost of ownership?
Answer: You have ignored the opportunity cost of the funds you are using for the down payment. By
using your $40,000 to buy the house, you give up the opportunity to earn interest on that money. If you
could earn 5% interest, then the opportunity cost is 0.05 x $40,000 = $2,000 per year, or $167 per month.
This does not imply that you should not buy this house. It does imply, however, that you need to think
carefully about opportunity cost as you weigh this decision. An economist would tell you that the monthly
cost of owning this home is $950 + $167 = $1,017.
3. You have 40,000 frequent flier miles. You could exchange your miles for a round trip ticket to
Bermuda over spring break. Does that mean your flight to Bermuda would be free? Explain your
reasoning.
Answer: It does not. You could use your miles for other travel and so there is an opportunity cost if you
use your miles to fly to Bermuda. Suppose, for example, you are definitely going to fly to Chicago when
the spring semester is over. You could use your 40,000 miles to fly to Chicago or you could purchase a
ticket for $300. In this case, the opportunity cost of using your miles to fly to Bermuda is the $300 you
will have to spend for the airfare to Chicago.
4. You have decided that you are going to consume 600 calories of beer and snacks at a party Saturday
night. A beer has 150 calories and a snack has 75 calories.
a. Create a table that shows the various combinations of beer and snacks you can consume. To keep
things simple, use only round numbers (e.g., you could choose 1 or 2 beers but not 1.5 beers).
b. What is the opportunity cost of a beer?
Problems
1. You have already purchased (non-refundable and unsellable) tickets to a concert on Friday night. A
friend also invites you to her birthday party on Friday. While you like your friend, you politely
decline because you really want to go to the concert.
a. You learn that your friend is serving flank steak at her party, all-you-can eat and at no charge.
Flank steak is your favorite food. Should this affect your decision to go to the concert? Explain by
using the term “opportunity cost.”
b. Suppose instead that you notice that the non-refundable concert ticket (that you already
purchased) cost you $10; previously you had mistakenly believed the price was $100. Should
learning this information affect your decision to go to the concert?
Answer:
a. This should affect your decision, or at least make you reconsider. The explicit cost of the concert
has not changed, nor the benefit of the concert itself. However, the opportunity cost of missing
the party is now higher than you previously thought.
b. This should not affect your decision. Whether you paid ($10 or $100) in the past is irrelevant to
the costs and benefits that you can affect by going (or not going) to the concert.
2. You are thinking about buying a house. You find one you like that costs $200,000. You learn that
your bank will give you a mortgage for $160,000 and that you would have to use all of your savings
to make the down payment of $40,000. You calculate that the mortgage payments, property taxes,
insurance, maintenance, and utilities would total $950 per month. Is $950 the cost of owning the
house? What important factor(s) have you left out of your calculation of the cost of ownership?
Answer: You have ignored the opportunity cost of the funds you are using for the down payment. By
using your $40,000 to buy the house, you give up the opportunity to earn interest on that money. If you
could earn 5% interest, then the opportunity cost is 0.05 x $40,000 = $2,000 per year, or $167 per month.
This does not imply that you should not buy this house. It does imply, however, that you need to think
carefully about opportunity cost as you weigh this decision. An economist would tell you that the monthly
cost of owning this home is $950 + $167 = $1,017.
3. You have 40,000 frequent flier miles. You could exchange your miles for a round trip ticket to
Bermuda over spring break. Does that mean your flight to Bermuda would be free? Explain your
reasoning.
Answer: It does not. You could use your miles for other travel and so there is an opportunity cost if you
use your miles to fly to Bermuda. Suppose, for example, you are definitely going to fly to Chicago when
the spring semester is over. You could use your 40,000 miles to fly to Chicago or you could purchase a
ticket for $300. In this case, the opportunity cost of using your miles to fly to Bermuda is the $300 you
will have to spend for the airfare to Chicago.
4. You have decided that you are going to consume 600 calories of beer and snacks at a party Saturday
night. A beer has 150 calories and a snack has 75 calories.
a. Create a table that shows the various combinations of beer and snacks you can consume. To keep
things simple, use only round numbers (e.g., you could choose 1 or 2 beers but not 1.5 beers).
b. What is the opportunity cost of a beer?
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Chapter 1 | The Principles and Practice of Economics 5
Answer:
a. Suppose you choose to consume 0 beers. Then you could use all 600 calories on snacks. Since
snacks have 75 calories you could consume 600 / 75 = 8 snacks. Now suppose you choose 1 beer.
A beer has 150 calories and so you would be left with 600 – 150 = 450 calories for snacks. You
could therefore consume 450 / 75 = 6 snacks if you choose 1 beer. You can use the same logic to
complete the table below.
Beer Snacks
0 8
1 6
2 4
3 2
4 0
b. If you consume 1 more beer you will have 150 fewer calories for snacks. Since a snack has 75
calories, consuming one more beer means that you will have to give up 150 / 75 = 2 snacks. The
opportunity cost of a beer is therefore 2 snacks.
5. Suppose you are ready to check out and see two lines: Line A has 3 people, while line B has 5 people.
a. Assume people just chose lines at random and have not yet had a chance to switch lines. Would
you consider this situation to be in equilibrium? Why or why not?
b. Assume that all 8 shoppers are optimizing (i.e., they have had a chance to switch), and that the
situation is in equilibrium. What conclusions would you draw?
c. Of all 8 shoppers, whose behavior is the most informative?
Answer:
a. This situation is not in equilibrium. Assuming both lines move at the same speed, it would make
sense for the last person in the longer line to switch to the shorter line.
b. If the 8 shoppers know what they are doing, then it must be the case that the shorter line moves
more slowly.
c. The behavior of the last person in each line is the most informative. The assumption that these
shoppers are optimizing allows an outside observer to draw conclusions about the speed of the
two lines.
6. Consider the following three statements:
i. You can either stand during a college football game or you can sit. You believe that you will
see the game very well if you stand and others sit but that you will not be able to see at all if
you sit and others stand. You therefore decide to stand.
ii. Your friend tells you that he expects many people to stand at football games.
iii. An economist studies photos of many college football games and estimates that 75 percent of
all fans stand and 25 percent sit.
Which of these statements deals with optimization, which deals with equilibrium, and which deals
with empiricism? Explain.
Answer:
a. Suppose you choose to consume 0 beers. Then you could use all 600 calories on snacks. Since
snacks have 75 calories you could consume 600 / 75 = 8 snacks. Now suppose you choose 1 beer.
A beer has 150 calories and so you would be left with 600 – 150 = 450 calories for snacks. You
could therefore consume 450 / 75 = 6 snacks if you choose 1 beer. You can use the same logic to
complete the table below.
Beer Snacks
0 8
1 6
2 4
3 2
4 0
b. If you consume 1 more beer you will have 150 fewer calories for snacks. Since a snack has 75
calories, consuming one more beer means that you will have to give up 150 / 75 = 2 snacks. The
opportunity cost of a beer is therefore 2 snacks.
5. Suppose you are ready to check out and see two lines: Line A has 3 people, while line B has 5 people.
a. Assume people just chose lines at random and have not yet had a chance to switch lines. Would
you consider this situation to be in equilibrium? Why or why not?
b. Assume that all 8 shoppers are optimizing (i.e., they have had a chance to switch), and that the
situation is in equilibrium. What conclusions would you draw?
c. Of all 8 shoppers, whose behavior is the most informative?
Answer:
a. This situation is not in equilibrium. Assuming both lines move at the same speed, it would make
sense for the last person in the longer line to switch to the shorter line.
b. If the 8 shoppers know what they are doing, then it must be the case that the shorter line moves
more slowly.
c. The behavior of the last person in each line is the most informative. The assumption that these
shoppers are optimizing allows an outside observer to draw conclusions about the speed of the
two lines.
6. Consider the following three statements:
i. You can either stand during a college football game or you can sit. You believe that you will
see the game very well if you stand and others sit but that you will not be able to see at all if
you sit and others stand. You therefore decide to stand.
ii. Your friend tells you that he expects many people to stand at football games.
iii. An economist studies photos of many college football games and estimates that 75 percent of
all fans stand and 25 percent sit.
Which of these statements deals with optimization, which deals with equilibrium, and which deals
with empiricism? Explain.
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Chapter 1 | The Principles and Practice of Economics 6
Answer: The first statement involves optimization. You believe that you will be best off if you stand
regardless of the decisions other people make. The second statement involves equilibrium. If many other
people also reason as you did then we should expect many people will decide to stand. The third
statement involves empiricism. Our theory tells us that we should expect many people to stand at games.
This economist’s empirical study supports the theory.
7. In 2014, California was in its third year of a major drought. With water supplies dwindling, Governor
Brown issued a plea for a voluntary 20 percent reduction in water use. This target was not reached. In
early 2015 Governor Brown issued an executive order requiring local water agencies to reduce water
use by 25 percent, but no enforcement mechanism was specified. No taxes or fines were in the
executive order. State officials hoped that they could achieve compliance without resorting to fines.
a. From an individual homeowner’s perspective, what are the costs and benefits of using water
during a drought? Why do you think that the voluntary reduction order in 2014 didn’t work?
b. Using concepts from this chapter, explain how you might get individual homeowners to reduce
water use during a drought.
c. Eventually, many communities began levying fines on water use. However, while many middle
income families dramatically cut water use, wealthy households cut back their water use
relatively little. How can you explain this phenomenon from an economic perspective?
Answers:
a. With no specific enforcement mechanism, there is low cost to using water. Water bills are not
zero, but these prices were low enough in the past to create a water shortage, so clearly the
financial cost is not high enough to prevent a shortage. There may be some social stigma attached
to watering a lawn, though this cost varies for each person and depends on their sense of civic
responsibility. On the flip side, the benefits of using water are quite clear: Green lawns, pleasant
showers, and odorless toilets. The fact that the 2014 plea did not work is because the cost of
violating a call for civic responsibility is not very high for most people.
b. Charging a higher price for water than in 2014 would likely result in a reduction in water usage.
When the price goes up, people would discover that some of their usage is actually not that
important.
c. Fines are equivalent to a higher price for water. In this case, lower income individuals were more
price elastic; they responded more sharply to a price change. This implies that the willingness to
pay for the last gallon of water in a low-income household is less than the willingness to pay in a
high-income household.
8. An economist observes that many students spend $100,000 to go to college. This researcher could ask
whether such spending is worth it, or she could assume that it is worth it. In other words, she could
assume that students are optimizing and that the education system is in equilibrium. What can the
economist conclude about the value of a college education?
Answer: An economist will conclude that college increases earnings (over a lifetime) by at least $100,000
-- the increase may be higher, but it cannot be lower. If this were not the case then students would choose
to skip college. This analysis assumes there are no other benefits to college besides higher income; as well
as no other costs besides monetary costs. In reality there are many other costs and benefits of college.
However, the main point stands: The observation that people are willing to pay a certain amount for
college provides information about the economic value of college.
9. It is the night before your economics final exam and you must decide how many hours to study. The
total benefits column shows how many more points you expect to earn because of increased
knowledge. The cost column shows how many points you will lose because of careless errors due to
Answer: The first statement involves optimization. You believe that you will be best off if you stand
regardless of the decisions other people make. The second statement involves equilibrium. If many other
people also reason as you did then we should expect many people will decide to stand. The third
statement involves empiricism. Our theory tells us that we should expect many people to stand at games.
This economist’s empirical study supports the theory.
7. In 2014, California was in its third year of a major drought. With water supplies dwindling, Governor
Brown issued a plea for a voluntary 20 percent reduction in water use. This target was not reached. In
early 2015 Governor Brown issued an executive order requiring local water agencies to reduce water
use by 25 percent, but no enforcement mechanism was specified. No taxes or fines were in the
executive order. State officials hoped that they could achieve compliance without resorting to fines.
a. From an individual homeowner’s perspective, what are the costs and benefits of using water
during a drought? Why do you think that the voluntary reduction order in 2014 didn’t work?
b. Using concepts from this chapter, explain how you might get individual homeowners to reduce
water use during a drought.
c. Eventually, many communities began levying fines on water use. However, while many middle
income families dramatically cut water use, wealthy households cut back their water use
relatively little. How can you explain this phenomenon from an economic perspective?
Answers:
a. With no specific enforcement mechanism, there is low cost to using water. Water bills are not
zero, but these prices were low enough in the past to create a water shortage, so clearly the
financial cost is not high enough to prevent a shortage. There may be some social stigma attached
to watering a lawn, though this cost varies for each person and depends on their sense of civic
responsibility. On the flip side, the benefits of using water are quite clear: Green lawns, pleasant
showers, and odorless toilets. The fact that the 2014 plea did not work is because the cost of
violating a call for civic responsibility is not very high for most people.
b. Charging a higher price for water than in 2014 would likely result in a reduction in water usage.
When the price goes up, people would discover that some of their usage is actually not that
important.
c. Fines are equivalent to a higher price for water. In this case, lower income individuals were more
price elastic; they responded more sharply to a price change. This implies that the willingness to
pay for the last gallon of water in a low-income household is less than the willingness to pay in a
high-income household.
8. An economist observes that many students spend $100,000 to go to college. This researcher could ask
whether such spending is worth it, or she could assume that it is worth it. In other words, she could
assume that students are optimizing and that the education system is in equilibrium. What can the
economist conclude about the value of a college education?
Answer: An economist will conclude that college increases earnings (over a lifetime) by at least $100,000
-- the increase may be higher, but it cannot be lower. If this were not the case then students would choose
to skip college. This analysis assumes there are no other benefits to college besides higher income; as well
as no other costs besides monetary costs. In reality there are many other costs and benefits of college.
However, the main point stands: The observation that people are willing to pay a certain amount for
college provides information about the economic value of college.
9. It is the night before your economics final exam and you must decide how many hours to study. The
total benefits column shows how many more points you expect to earn because of increased
knowledge. The cost column shows how many points you will lose because of careless errors due to
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Chapter 1 | The Principles and Practice of Economics 7
lack of sleep. (The “marginal” columns show the effect of each additional hour spent studying. These
marginal numbers are calculated by taking the difference within a column from one row to the next
row.)
Hours Spent
Studying Total Benefit Marginal Benefit Total Cost Marginal Cost
0 0 -- 0 --
1 10 10 0 0
2 16 6 3 3
3 20 4 8 5
4 20 0 15 7
a. If you study in an optimal way, how many more points will you earn on the test?
b. Explain how you can find the optimal number of hours by using the marginal benefits and
marginal costs columns.
Answer:
a. Total benefit minus total cost is maximized at 16 - 3 = 13 when you study for two hours. This
difference is lower in all other rows.
b. You can arrive at the answer of 2 hours by noticing that the first hour is well worth it since the
marginal benefit of 10 is greater than the marginal cost of 0. The second hour is also worth it
since 6 > 3. However, the third hour is not worth it since 4 < 5, thus you will gain fewer points
than you will lose. (This sort of “marginal analysis” is a recurrent theme in economics.)
lack of sleep. (The “marginal” columns show the effect of each additional hour spent studying. These
marginal numbers are calculated by taking the difference within a column from one row to the next
row.)
Hours Spent
Studying Total Benefit Marginal Benefit Total Cost Marginal Cost
0 0 -- 0 --
1 10 10 0 0
2 16 6 3 3
3 20 4 8 5
4 20 0 15 7
a. If you study in an optimal way, how many more points will you earn on the test?
b. Explain how you can find the optimal number of hours by using the marginal benefits and
marginal costs columns.
Answer:
a. Total benefit minus total cost is maximized at 16 - 3 = 13 when you study for two hours. This
difference is lower in all other rows.
b. You can arrive at the answer of 2 hours by noticing that the first hour is well worth it since the
marginal benefit of 10 is greater than the marginal cost of 0. The second hour is also worth it
since 6 > 3. However, the third hour is not worth it since 4 < 5, thus you will gain fewer points
than you will lose. (This sort of “marginal analysis” is a recurrent theme in economics.)
Loading page 9...
Chapter 2
Economic Methods and Economic
Questions
Questions
1. What does it mean to say that economists use the scientific method? How do economists distinguish
between models that work and those that don’t?
Answer: The scientific method is the name for the ongoing process that economists and other scientists
use to develop models of the world, test those models with data, and evaluate how well the models predict
behavior. While this process may not reveal the ‘true’ model of the world, it does help identify models
that are useful in understanding the world.
In order to decide whether models make accurate predictions or not, economists test them against real-
world data. Data are facts, measurements, or statistics that describe the world. This process of testing
models against data is called empiricism.
2. What is meant by empiricism?
Answer: Empirical evidence is a set of facts established by observation and measurement, which are used
to evaluate a model. Empiricism refers to the practice of using data to test economic models. When
conducting empirical analysis, economists refer to a model’s predictions as hypotheses. Hypotheses are
predictions (typically generated by a model) that can be tested with data.
3. What are two important properties of economic models? Models tend to be simplified descriptions of
a real-world phenomenon. Does this mean that they are unrealistic?
Answer: A good economic model has two important properties. First, it is an approximation. The model
predicts what would happen on average. Second, it makes predictions that can be falsified by data.
A model is a simplified description, or representation, of reality. Because models are simplified, they are
not perfect replicas of reality. However, this does not mean that they are unrealistic. Models are usually
simplified in order to be able to isolate the relationship between two variables. Even if a model is based
on simplified assumptions, it may still help us make good predictions.
4. Suppose 5,000 people bought popsicles on a hot summer day. If the average number of popsicles that
each person bought is 2, how many popsicles were sold that day?
Answer: The mean is calculated as the sum of all the different items divided by the number of items. The
average value is the sum of all popsicles sold divided by the number of people who bought them. If each
of the 5,000 people bought an average of 2 popsicles, that implies that 10,000 popsicles were sold that
day.
5. How does the sample size affect the validity of an empirical argument? When is it acceptable to use
only one example to disprove a statement?
Answer: The size of the sample used to test the argument can affect the results. A small sample may mean
no conclusions can be drawn from a study. A key strength of economic analysis is the amount of data
used. Using a large number of observations strengthens the force of an empirical argument. For example,
Economic Methods and Economic
Questions
Questions
1. What does it mean to say that economists use the scientific method? How do economists distinguish
between models that work and those that don’t?
Answer: The scientific method is the name for the ongoing process that economists and other scientists
use to develop models of the world, test those models with data, and evaluate how well the models predict
behavior. While this process may not reveal the ‘true’ model of the world, it does help identify models
that are useful in understanding the world.
In order to decide whether models make accurate predictions or not, economists test them against real-
world data. Data are facts, measurements, or statistics that describe the world. This process of testing
models against data is called empiricism.
2. What is meant by empiricism?
Answer: Empirical evidence is a set of facts established by observation and measurement, which are used
to evaluate a model. Empiricism refers to the practice of using data to test economic models. When
conducting empirical analysis, economists refer to a model’s predictions as hypotheses. Hypotheses are
predictions (typically generated by a model) that can be tested with data.
3. What are two important properties of economic models? Models tend to be simplified descriptions of
a real-world phenomenon. Does this mean that they are unrealistic?
Answer: A good economic model has two important properties. First, it is an approximation. The model
predicts what would happen on average. Second, it makes predictions that can be falsified by data.
A model is a simplified description, or representation, of reality. Because models are simplified, they are
not perfect replicas of reality. However, this does not mean that they are unrealistic. Models are usually
simplified in order to be able to isolate the relationship between two variables. Even if a model is based
on simplified assumptions, it may still help us make good predictions.
4. Suppose 5,000 people bought popsicles on a hot summer day. If the average number of popsicles that
each person bought is 2, how many popsicles were sold that day?
Answer: The mean is calculated as the sum of all the different items divided by the number of items. The
average value is the sum of all popsicles sold divided by the number of people who bought them. If each
of the 5,000 people bought an average of 2 popsicles, that implies that 10,000 popsicles were sold that
day.
5. How does the sample size affect the validity of an empirical argument? When is it acceptable to use
only one example to disprove a statement?
Answer: The size of the sample used to test the argument can affect the results. A small sample may mean
no conclusions can be drawn from a study. A key strength of economic analysis is the amount of data
used. Using a large number of observations strengthens the force of an empirical argument. For example,
Loading page 10...
Chapter 2 | Economic Methods and Economic Questions 10
if you collect information on consumption from 20,000 people as opposed to 20 people, you are likely to
get a more representative result. However, a single example can be used to contradict a statement.
6. Explain why correlation does not always imply causation. Does causation always imply positive
correlation? Explain your answer.
Answer: Correlation means that there is a relationship between two variables; as one variable changes,
another variable changes. Causation occurs when one variable directly affects another through a cause-
and-effect relationship. Correlation suggests that there is some kind of connection, but not necessarily a
cause and an effect. For example, number of storks in a region might be correlated with the number of
babies born in the region. But this doesn’t mean that storks bring babies.
Positive correlation implies that two variables tend to move in the same direction. However, causation
need not only imply positive correlation. For example, sleeping an extra hour per night may improve your
energy level at work. However, this positive relationship is swamped by the fact that people who sleep a
ton tend to be low energy; thus hours of sleep and energy will be negatively correlated even though there
is a positive causal link.
7. Give an example of a pair of variables that have a positive correlation, a pair of variables that have a
negative correlation, and a pair of variables that have zero correlation.
Answer: A person’s IQ and his or her telephone number are likely to show zero correlation. The number
of winter coats sold and the average temperature in a region are likely to show a negative correlation. The
quantity of fertilizers used and crop yield (e.g., the number of bushels of wheat grown per acre) are likely
to have a positive correlation.
8. What is meant by randomization? How does randomization affect the results of an experiment?
Answer: Randomization is the assignment of subjects by chance, rather than by choice, to the effect of a
treatment. Assigning participants randomly will ensure that the result of the experiment is not biased.
When randomization is employed, correlation does imply causation: How else can a positive correlation
be explained? There is no other way (assuming perfect random assignment) except with a causal link
between the treatment and the outcome.
9. This chapter discussed natural and randomized experiments. How does a natural experiment differ
from a randomized one?
Answer: A natural experiment is an empirical study in which some process – out of the control of the
experimenter – has assigned subjects to control and test groups in a random or nearly random way. The
process of randomization involves the assignment of subjects by chance, rather than by choice, to a test
group or control group.
10. Suppose you had to find the effect of seat belt rules on road accident fatalities. Would you choose to
run a randomized experiment or would it make sense to use natural experiments here? Explain.
Answer: It would be difficult (and, in many people’s view, unethical) to conduct a randomized
experiment. Instead, the study should use a natural experiment. You can study data on the causes of road
accident fatalities in cities where seat belt rules were not enforced, or in cities that have recently adopted
new, more stringent seat belt laws. Controlling for other factors like an increase in the number of cars,
etc., you can then look at similar data when seat belt rules have been implemented.
Problems
1. Although the mean and median are closely related, the difference between the mean and the median is
sometimes of interest.
if you collect information on consumption from 20,000 people as opposed to 20 people, you are likely to
get a more representative result. However, a single example can be used to contradict a statement.
6. Explain why correlation does not always imply causation. Does causation always imply positive
correlation? Explain your answer.
Answer: Correlation means that there is a relationship between two variables; as one variable changes,
another variable changes. Causation occurs when one variable directly affects another through a cause-
and-effect relationship. Correlation suggests that there is some kind of connection, but not necessarily a
cause and an effect. For example, number of storks in a region might be correlated with the number of
babies born in the region. But this doesn’t mean that storks bring babies.
Positive correlation implies that two variables tend to move in the same direction. However, causation
need not only imply positive correlation. For example, sleeping an extra hour per night may improve your
energy level at work. However, this positive relationship is swamped by the fact that people who sleep a
ton tend to be low energy; thus hours of sleep and energy will be negatively correlated even though there
is a positive causal link.
7. Give an example of a pair of variables that have a positive correlation, a pair of variables that have a
negative correlation, and a pair of variables that have zero correlation.
Answer: A person’s IQ and his or her telephone number are likely to show zero correlation. The number
of winter coats sold and the average temperature in a region are likely to show a negative correlation. The
quantity of fertilizers used and crop yield (e.g., the number of bushels of wheat grown per acre) are likely
to have a positive correlation.
8. What is meant by randomization? How does randomization affect the results of an experiment?
Answer: Randomization is the assignment of subjects by chance, rather than by choice, to the effect of a
treatment. Assigning participants randomly will ensure that the result of the experiment is not biased.
When randomization is employed, correlation does imply causation: How else can a positive correlation
be explained? There is no other way (assuming perfect random assignment) except with a causal link
between the treatment and the outcome.
9. This chapter discussed natural and randomized experiments. How does a natural experiment differ
from a randomized one?
Answer: A natural experiment is an empirical study in which some process – out of the control of the
experimenter – has assigned subjects to control and test groups in a random or nearly random way. The
process of randomization involves the assignment of subjects by chance, rather than by choice, to a test
group or control group.
10. Suppose you had to find the effect of seat belt rules on road accident fatalities. Would you choose to
run a randomized experiment or would it make sense to use natural experiments here? Explain.
Answer: It would be difficult (and, in many people’s view, unethical) to conduct a randomized
experiment. Instead, the study should use a natural experiment. You can study data on the causes of road
accident fatalities in cities where seat belt rules were not enforced, or in cities that have recently adopted
new, more stringent seat belt laws. Controlling for other factors like an increase in the number of cars,
etc., you can then look at similar data when seat belt rules have been implemented.
Problems
1. Although the mean and median are closely related, the difference between the mean and the median is
sometimes of interest.
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Chapter 2 | Economic Methods and Economic Questions 11
a. Suppose country A has five families. Their incomes are $10,000, $20,000, $30,000, $40,000, and
$50,000. What is the median family income in A? What is the mean income?
b. Country B also has five families. Their incomes are $10,000, $20,000, $30,000, $40,000, and
$150,000. What is the median family income in B? What is the mean income?
c. In which country is income inequality greater, A or B?
d. Suppose you thought income inequality in the US had increased over time. Based on your
answers to this question, would you expect that the ratio of the mean income in the US to the
median income has risen or fallen? Explain.
Answer:
a. We can find the mean by summing the observations and dividing by the number of observations.
So the mean income in Country A is ($10,000 + $20,000 + $30,000 + $40,000 + $50,000) / 5 =
$30,000. The median income is the income of the family in the middle of the income distribution.
The median income in Country A is $30,000. Two families have income below $30,000 and two
have income above $30,000.
b. A similar argument shows that the mean income in Country B is ($10,000 + $20,000 + $30,000 +
$40,000 + $150,000) / 5 = $50,000. Median income in B is $30,000; as in Country A, two
families have income below $30,000 and two have income above $30,000.
c. Income inequality is higher in Country B. The highest income family in Country B earns
$150,000, 60% of the total income in that country. The highest income family in A earns
$50,000, just 33% of total income in A. We found that the median income in the two countries
was the same but the mean income was very different. Means will be heavily influenced by
extreme values such as the incomes of the very wealthy; median income is less sensitive to
extremes. Economists sometimes use the ratio of the mean to median income in a country as a
rough measure of income inequality; higher values of this ratio reflect greater inequality.
d. You should expect to find that the ratio of the mean to median income has risen. As we argued
above, the mean is more sensitive than the median to the incomes of the very wealthy.
2. Consider the following situation: your math professor tells your class (of five students) that the mean
score on the final exam is 80 but the median is 100. How is that possible? Explain.
Answer: Typically, when the mean is lower than the median there is a skew in the data: The test scores
that were below the median were way below the median. For example, with only five tests, the median
may be 100 because three out of five people scored 100. If the lower scorers received scores of 40 and 60
then the average (i.e. the mean) will be (40+60+100+100+100)/5 = 80.
3. Suppose you come across a study that has discovered a correlation between reading books and life
expectancy: People who read more books live longer. Come up with at least one plausible way that
this correlation exists even though there is no direct causal link.
Answer: One possibility is that wealthier individuals can afford to spend more time reading; they also can
afford better medical care. Another possibility is that sitting in a quiet place is good for health, and
reading just happens to be one way to sit in a quiet place. Also, if you live longer you have more time to
read more books (reverse causality), though any reasonable study would account for this effect before
drawing conclusions.
4. Some studies have found that people who owned guns were more likely to be killed with a gun. Do
you think this study is strong evidence in favor of stricter gun control laws? Explain.
Answer: Not necessarily. It is quite possible that people who thought they were at risk (perhaps because
a. Suppose country A has five families. Their incomes are $10,000, $20,000, $30,000, $40,000, and
$50,000. What is the median family income in A? What is the mean income?
b. Country B also has five families. Their incomes are $10,000, $20,000, $30,000, $40,000, and
$150,000. What is the median family income in B? What is the mean income?
c. In which country is income inequality greater, A or B?
d. Suppose you thought income inequality in the US had increased over time. Based on your
answers to this question, would you expect that the ratio of the mean income in the US to the
median income has risen or fallen? Explain.
Answer:
a. We can find the mean by summing the observations and dividing by the number of observations.
So the mean income in Country A is ($10,000 + $20,000 + $30,000 + $40,000 + $50,000) / 5 =
$30,000. The median income is the income of the family in the middle of the income distribution.
The median income in Country A is $30,000. Two families have income below $30,000 and two
have income above $30,000.
b. A similar argument shows that the mean income in Country B is ($10,000 + $20,000 + $30,000 +
$40,000 + $150,000) / 5 = $50,000. Median income in B is $30,000; as in Country A, two
families have income below $30,000 and two have income above $30,000.
c. Income inequality is higher in Country B. The highest income family in Country B earns
$150,000, 60% of the total income in that country. The highest income family in A earns
$50,000, just 33% of total income in A. We found that the median income in the two countries
was the same but the mean income was very different. Means will be heavily influenced by
extreme values such as the incomes of the very wealthy; median income is less sensitive to
extremes. Economists sometimes use the ratio of the mean to median income in a country as a
rough measure of income inequality; higher values of this ratio reflect greater inequality.
d. You should expect to find that the ratio of the mean to median income has risen. As we argued
above, the mean is more sensitive than the median to the incomes of the very wealthy.
2. Consider the following situation: your math professor tells your class (of five students) that the mean
score on the final exam is 80 but the median is 100. How is that possible? Explain.
Answer: Typically, when the mean is lower than the median there is a skew in the data: The test scores
that were below the median were way below the median. For example, with only five tests, the median
may be 100 because three out of five people scored 100. If the lower scorers received scores of 40 and 60
then the average (i.e. the mean) will be (40+60+100+100+100)/5 = 80.
3. Suppose you come across a study that has discovered a correlation between reading books and life
expectancy: People who read more books live longer. Come up with at least one plausible way that
this correlation exists even though there is no direct causal link.
Answer: One possibility is that wealthier individuals can afford to spend more time reading; they also can
afford better medical care. Another possibility is that sitting in a quiet place is good for health, and
reading just happens to be one way to sit in a quiet place. Also, if you live longer you have more time to
read more books (reverse causality), though any reasonable study would account for this effect before
drawing conclusions.
4. Some studies have found that people who owned guns were more likely to be killed with a gun. Do
you think this study is strong evidence in favor of stricter gun control laws? Explain.
Answer: Not necessarily. It is quite possible that people who thought they were at risk (perhaps because
Loading page 12...
Chapter 2 | Economic Methods and Economic Questions 12
they live in dangerous neighborhoods) were more likely to buy a gun for self-protection. This is an
example of a case where correlation may not imply causation. There has been a good deal of research on
this question. See, for example, a Harvard School of Public Health 2011 interview with David Hemenway
(http://www.hsph.harvard.edu/news/features/review-guns-politics-hemenway).
5. As the text explains, it can sometimes be very difficult to sort out the direction of causality.
a. Why might you think more police officers would lead to lower crime rates? Why might you think
that higher crime rates would lead to more police officers?
b. In 2012, the New England Journal of Medicine published research that showed a strong
correlation between the consumption of chocolate in a country and the number of Nobel Prize
winners in that country. Do you think countries that want to encourage their citizens to win Nobel
Prizes should increase their consumption of chocolate?
c. A recent article in the Journal of Applied Physiology found that elderly runners had healthier
muscles than a comparison group of the same age. Although the members of the comparison
group were all still living independently, they had lower muscle mass and muscle strength than
the athletes. The popular press framed the article as proof that exercise causes people to be
healthier. Is that the only way to interpret causality in this example?
Answer:
a. There is a great deal of evidence that increasing the number of police officers in a neighborhood
can drive down crime. The police, for example, will deter criminals who realize the chances they
will be caught have gone up and the police may be able to head off conflicts between gangs.
Therefore more police could lead to less crime. Cities strategically assign more police to high
crime areas (since by definition, those are the areas where crimes are more likely to occur).
Therefore, more crime can lead to more police.
b. Correlation does not necessarily imply causation. A strong positive correlation between chocolate
consumption and Nobel Prize winners does not, by itself, suggest causation. It is possible that this
is a chance correlation. It may also be case that certain variables that could explain this
relationship have been omitted from the study.
c. Another quite likely story that would generate the same correlation between running and muscle
mass: Elderly people with enough muscle to go outside for a run are more likely to go outside for
a run! It is likely some people who lose muscle mass and respond by not running as much; in fact,
this almost surely happens. This argument is not definitive proof that the causal link from running
to muscle mass is false, but the study is also not definitive proof that the causal link is true.
See the June 11, 2013 New York Times article “Chicago Tactics Put Major Dent in Killing Trend”
(http://www.nytimes.com/2013/06/11/us/chicago-homicides-fall-by-34-percent-so-far-this-
year.html?hp) on the relationship between police and crime rates. See
http://www.reuters.com/article/2012/10/10/us-eat-chocolate-win-the-nobel-prize-
idUSBRE8991MS20121010 on the effects of eating chocolate.
6. The chapter shows that as a general rule people with more education earn higher salaries. Economists
have offered two explanations of this relationship. The human capital argument says that high schools
and colleges teach people valuable skills and employers are willing to pay higher salaries to attract
people with those skills. The signaling argument says that college graduates earn more because a
college degree is a signal to employers that a job applicant is diligent, intelligent, and persevering.
How might you use data on people with 2, 3, and 4 years of college education to shed light on this
controversy?
they live in dangerous neighborhoods) were more likely to buy a gun for self-protection. This is an
example of a case where correlation may not imply causation. There has been a good deal of research on
this question. See, for example, a Harvard School of Public Health 2011 interview with David Hemenway
(http://www.hsph.harvard.edu/news/features/review-guns-politics-hemenway).
5. As the text explains, it can sometimes be very difficult to sort out the direction of causality.
a. Why might you think more police officers would lead to lower crime rates? Why might you think
that higher crime rates would lead to more police officers?
b. In 2012, the New England Journal of Medicine published research that showed a strong
correlation between the consumption of chocolate in a country and the number of Nobel Prize
winners in that country. Do you think countries that want to encourage their citizens to win Nobel
Prizes should increase their consumption of chocolate?
c. A recent article in the Journal of Applied Physiology found that elderly runners had healthier
muscles than a comparison group of the same age. Although the members of the comparison
group were all still living independently, they had lower muscle mass and muscle strength than
the athletes. The popular press framed the article as proof that exercise causes people to be
healthier. Is that the only way to interpret causality in this example?
Answer:
a. There is a great deal of evidence that increasing the number of police officers in a neighborhood
can drive down crime. The police, for example, will deter criminals who realize the chances they
will be caught have gone up and the police may be able to head off conflicts between gangs.
Therefore more police could lead to less crime. Cities strategically assign more police to high
crime areas (since by definition, those are the areas where crimes are more likely to occur).
Therefore, more crime can lead to more police.
b. Correlation does not necessarily imply causation. A strong positive correlation between chocolate
consumption and Nobel Prize winners does not, by itself, suggest causation. It is possible that this
is a chance correlation. It may also be case that certain variables that could explain this
relationship have been omitted from the study.
c. Another quite likely story that would generate the same correlation between running and muscle
mass: Elderly people with enough muscle to go outside for a run are more likely to go outside for
a run! It is likely some people who lose muscle mass and respond by not running as much; in fact,
this almost surely happens. This argument is not definitive proof that the causal link from running
to muscle mass is false, but the study is also not definitive proof that the causal link is true.
See the June 11, 2013 New York Times article “Chicago Tactics Put Major Dent in Killing Trend”
(http://www.nytimes.com/2013/06/11/us/chicago-homicides-fall-by-34-percent-so-far-this-
year.html?hp) on the relationship between police and crime rates. See
http://www.reuters.com/article/2012/10/10/us-eat-chocolate-win-the-nobel-prize-
idUSBRE8991MS20121010 on the effects of eating chocolate.
6. The chapter shows that as a general rule people with more education earn higher salaries. Economists
have offered two explanations of this relationship. The human capital argument says that high schools
and colleges teach people valuable skills and employers are willing to pay higher salaries to attract
people with those skills. The signaling argument says that college graduates earn more because a
college degree is a signal to employers that a job applicant is diligent, intelligent, and persevering.
How might you use data on people with 2, 3, and 4 years of college education to shed light on this
controversy?
Loading page 13...
Chapter 2 | Economic Methods and Economic Questions 13
Answer: If the human capital explanation is correct, then we might expect to find that people who attend
college but do not graduate earn salaries that are close to what college graduates earn. Consider the
extreme case of people who drop out of college the week before graduation. It is very unlikely that they
would have improved their job skills much in that last week. The human capital school of thought would
suggest that they should therefore earn roughly the same salaries as college graduates. On the other hand,
the signaling school of thought would argue that these people should earn significantly less than college
graduates. Employers would interpret their failure to graduate as a signal they are not as diligent or
persevering as people who see their college educations through to the end. There is substantial literature
on what is often called the “sheepskin effect” (college diplomas used to be written on sheepskin; Notre
Dame continued to use sheepskin until 2012). That literature suggests that human capital and signaling
both contribute to the returns to education that we observe in the data.
For recent evidence, see the Michael Greenstone and Adam Looney 2013 Brookings Institution study “Is
Starting College and Not Finishing Really That Bad?”
(http://www.brookings.edu/blogs/jobs/posts/2013/06/07-return-to-some-college-greenstone-looney). They
find that people with some college education but who do not graduate from college earn an average of
$8,000 more per year than high school graduates who never attend college.
7. You decide to run an experiment. You invite 50 friends to a party. You randomly select 25 friends
and tell them that there will be free food; most of them show up to your party. For the other 25 friends
you do not mention the free food; none of these friends show up. Based on the correlation in your
data, you conclude that free food causes people to come to parties. A buddy points out “be careful,
correlation does not imply causation.” How should you respond?
Answer: Assuming you really did choose the two groups randomly, then the correlation does in fact imply
causation. If your friend challenges you, ask him “what else could it be?” Given randomization, the
relationship is not due to omitted variables, nor is it due to reverse causality. (It is possible that due to a
small sample you just happened to get a spurious correlation, but this is another matter related to
statistical inference, not correlation vs causation.)
8. Oregon expanded its Medicaid coverage in 2008. Roughly 90,000 people applied but the state had
funds to cover only an additional 30,000 people (who were randomly chosen from the total applicant
pool of 90,000). How could you use the Oregon experience to estimate the impact of increased access
to health care on health outcomes?
Answer: The Oregon experience is a natural experiment. The state chose people randomly from the pool
of applicants, and so on average the new Medicaid recipients were very similar to the people who applied
but were turned down. By tracking the health outcomes of people in these two groups we can study the
effect of better access to health care.
See “Medicaid Access Increases Use of Care, Study Finds,” New York Times, May 1, 2013
(http://www.nytimes.com/2013/05/02/business/study-finds-health-care-use-rises-with-expanded-
medicaid.html?_r=0).
9. A simple economic model predicts that a fall in the price of bus tickets means that more people will
take the bus. However, you observe that some people still do not take the bus even after the price of a
ticket fell.
a. Is the model incorrect?
b. How would you test this model?
Answer:
a. The model is not necessarily incorrect. Models are only approximations of real-life behavior.
Even very good models make predictions that are often correct. So, on average, more people will
Answer: If the human capital explanation is correct, then we might expect to find that people who attend
college but do not graduate earn salaries that are close to what college graduates earn. Consider the
extreme case of people who drop out of college the week before graduation. It is very unlikely that they
would have improved their job skills much in that last week. The human capital school of thought would
suggest that they should therefore earn roughly the same salaries as college graduates. On the other hand,
the signaling school of thought would argue that these people should earn significantly less than college
graduates. Employers would interpret their failure to graduate as a signal they are not as diligent or
persevering as people who see their college educations through to the end. There is substantial literature
on what is often called the “sheepskin effect” (college diplomas used to be written on sheepskin; Notre
Dame continued to use sheepskin until 2012). That literature suggests that human capital and signaling
both contribute to the returns to education that we observe in the data.
For recent evidence, see the Michael Greenstone and Adam Looney 2013 Brookings Institution study “Is
Starting College and Not Finishing Really That Bad?”
(http://www.brookings.edu/blogs/jobs/posts/2013/06/07-return-to-some-college-greenstone-looney). They
find that people with some college education but who do not graduate from college earn an average of
$8,000 more per year than high school graduates who never attend college.
7. You decide to run an experiment. You invite 50 friends to a party. You randomly select 25 friends
and tell them that there will be free food; most of them show up to your party. For the other 25 friends
you do not mention the free food; none of these friends show up. Based on the correlation in your
data, you conclude that free food causes people to come to parties. A buddy points out “be careful,
correlation does not imply causation.” How should you respond?
Answer: Assuming you really did choose the two groups randomly, then the correlation does in fact imply
causation. If your friend challenges you, ask him “what else could it be?” Given randomization, the
relationship is not due to omitted variables, nor is it due to reverse causality. (It is possible that due to a
small sample you just happened to get a spurious correlation, but this is another matter related to
statistical inference, not correlation vs causation.)
8. Oregon expanded its Medicaid coverage in 2008. Roughly 90,000 people applied but the state had
funds to cover only an additional 30,000 people (who were randomly chosen from the total applicant
pool of 90,000). How could you use the Oregon experience to estimate the impact of increased access
to health care on health outcomes?
Answer: The Oregon experience is a natural experiment. The state chose people randomly from the pool
of applicants, and so on average the new Medicaid recipients were very similar to the people who applied
but were turned down. By tracking the health outcomes of people in these two groups we can study the
effect of better access to health care.
See “Medicaid Access Increases Use of Care, Study Finds,” New York Times, May 1, 2013
(http://www.nytimes.com/2013/05/02/business/study-finds-health-care-use-rises-with-expanded-
medicaid.html?_r=0).
9. A simple economic model predicts that a fall in the price of bus tickets means that more people will
take the bus. However, you observe that some people still do not take the bus even after the price of a
ticket fell.
a. Is the model incorrect?
b. How would you test this model?
Answer:
a. The model is not necessarily incorrect. Models are only approximations of real-life behavior.
Even very good models make predictions that are often correct. So, on average, more people will
Loading page 14...
Chapter 2 | Economic Methods and Economic Questions 14
take the bus. The model is also likely to have made some assumptions, such as no change in costs
of other types of transport, or that people have no specific preferences and cost is the only
determinant of the mode of transport used. In reality, some of these assumptions may be violated
which could explain why a fall in the price of bus tickets does not induce everyone to take the
bus. That does not imply that the model’s conclusion is incorrect. In situations where the
assumptions it makes are satisfied, its prediction will often be correct.
b. The hypothesis here states that as bus prices fall, the number of passengers who take the bus will
increase. A natural experiment can be used to test this model. You can use data on price changes
and changes in revenues earned from tickets to see whether the model is accurate.
take the bus. The model is also likely to have made some assumptions, such as no change in costs
of other types of transport, or that people have no specific preferences and cost is the only
determinant of the mode of transport used. In reality, some of these assumptions may be violated
which could explain why a fall in the price of bus tickets does not induce everyone to take the
bus. That does not imply that the model’s conclusion is incorrect. In situations where the
assumptions it makes are satisfied, its prediction will often be correct.
b. The hypothesis here states that as bus prices fall, the number of passengers who take the bus will
increase. A natural experiment can be used to test this model. You can use data on price changes
and changes in revenues earned from tickets to see whether the model is accurate.
Loading page 15...
Chapter 2 | Economic Methods and Economic Questions 15
A1. How would you represent the following graphically?
a. Income inequality in the U.S. has increased over the past 10 years.
b. All the workers in the manufacturing sector in a particular country fit into one (and only one) of
the following categories: 31.5 percent are high school dropouts, 63.5 percent have a high school
diploma, and the rest have vocational training certificates.
c. The median income of a household in Alabama was $43,464 in 2012, and the median income of a
household in Connecticut was $64,247 in 2012.
Answer:
a. Since the graph needs to show how income inequality increases over a period of time, a time-
series graph needs to be used here.
b. A pie chart is a circular chart split into segments to show the percentages of parts to the whole.
Since the given data is in percentages, a pie-chart can be used to represent each category of
workers.
c. A bar chart would be a good way to compare income in Alabama and Connecticut. The height of
each bar would represent the income in each one of the states.
A2. Consider the following data that shows the quantity of coffee produced in Brazil from 2004-2012.
Year Production (in tons)
2004 2,465,710
2005 2,140,169
2006 2,573,368
2007 2,249,011
2008 2,796,927
2009 2,440,056
2010 2,907,265
2011 2,700,440
2012 3,037,534
a. Plot the data in a time series graph.
b. What is the mean quantity of coffee that Brazil produced from 2009 to 2011?
c. In percentage terms, how much has the 2012 crop increased over the 2009-2011 mean?
Answer:
a. A time-series graph can be used to represent the quantity of coffee produced from 2004 to 2012.
A1. How would you represent the following graphically?
a. Income inequality in the U.S. has increased over the past 10 years.
b. All the workers in the manufacturing sector in a particular country fit into one (and only one) of
the following categories: 31.5 percent are high school dropouts, 63.5 percent have a high school
diploma, and the rest have vocational training certificates.
c. The median income of a household in Alabama was $43,464 in 2012, and the median income of a
household in Connecticut was $64,247 in 2012.
Answer:
a. Since the graph needs to show how income inequality increases over a period of time, a time-
series graph needs to be used here.
b. A pie chart is a circular chart split into segments to show the percentages of parts to the whole.
Since the given data is in percentages, a pie-chart can be used to represent each category of
workers.
c. A bar chart would be a good way to compare income in Alabama and Connecticut. The height of
each bar would represent the income in each one of the states.
A2. Consider the following data that shows the quantity of coffee produced in Brazil from 2004-2012.
Year Production (in tons)
2004 2,465,710
2005 2,140,169
2006 2,573,368
2007 2,249,011
2008 2,796,927
2009 2,440,056
2010 2,907,265
2011 2,700,440
2012 3,037,534
a. Plot the data in a time series graph.
b. What is the mean quantity of coffee that Brazil produced from 2009 to 2011?
c. In percentage terms, how much has the 2012 crop increased over the 2009-2011 mean?
Answer:
a. A time-series graph can be used to represent the quantity of coffee produced from 2004 to 2012.
Loading page 16...
Chapter 2 | Economic Methods and Economic Questions 16
b. The average quantity of coffee that Brazil produced during the 2009-11 period is 2,682,589 587
tons. This is the sum of the total quantity produced divided by the number of years.
c. The coffee crop in 2012 is 14.6% larger than the average coffee crop in 2009-2011. The increase
in production is 3,073,534 – 2,682,589 = 390,945. In percentage terms, the change is 390,945 /
2,682,589 587 = 14.6%.
Data taken from: http://faostat.fao.org/site/567/default.aspx#ancor
A3. Suppose the following table shows the relationship between revenue that the Girl Scouts earn and the
number of cookie boxes that they sell.
Number of cookie
boxes Revenue ($)
50 200
150 600
250 1,000
350 1,400
450 1,800
550 2,200
a. Present the data in a scatter plot.
b. Do the two variables have a positive relationship or do they have a negative relationship?
Explain.
c. What is the slope of the line that you get in the scatter plot? What does the slope imply about the
price of a box of Girl Scout cookies?
Answer:
a. The following line chart shows the relationship between the Girl Scouts’ revenue and the number
of cookie boxes that they sell:
b. The average quantity of coffee that Brazil produced during the 2009-11 period is 2,682,589 587
tons. This is the sum of the total quantity produced divided by the number of years.
c. The coffee crop in 2012 is 14.6% larger than the average coffee crop in 2009-2011. The increase
in production is 3,073,534 – 2,682,589 = 390,945. In percentage terms, the change is 390,945 /
2,682,589 587 = 14.6%.
Data taken from: http://faostat.fao.org/site/567/default.aspx#ancor
A3. Suppose the following table shows the relationship between revenue that the Girl Scouts earn and the
number of cookie boxes that they sell.
Number of cookie
boxes Revenue ($)
50 200
150 600
250 1,000
350 1,400
450 1,800
550 2,200
a. Present the data in a scatter plot.
b. Do the two variables have a positive relationship or do they have a negative relationship?
Explain.
c. What is the slope of the line that you get in the scatter plot? What does the slope imply about the
price of a box of Girl Scout cookies?
Answer:
a. The following line chart shows the relationship between the Girl Scouts’ revenue and the number
of cookie boxes that they sell:
Loading page 17...
Chapter 2 | Economic Methods and Economic Questions 17
b. Since the values of both variables increase together in the same direction, they have a positive
relationship. This means that as more cookie boxes are sold, the revenue earned increases.
c. The slope is constant in this problem and so we can choose any two points to calculate the slope.
Suppose we use the first and last data points. The slope is calculated as
. The slope implies that one extra box of
cookies sold is associated with $4 more in revenue.
b. Since the values of both variables increase together in the same direction, they have a positive
relationship. This means that as more cookie boxes are sold, the revenue earned increases.
c. The slope is constant in this problem and so we can choose any two points to calculate the slope.
Suppose we use the first and last data points. The slope is calculated as
. The slope implies that one extra box of
cookies sold is associated with $4 more in revenue.
Loading page 18...
Chapter 3
Optimization: Doing the Best You Can
Questions
1. What is meant by optimization? Compare and contrast optimization using total value and
optimization using marginal analysis.
Answer: Optimization is the process that describes almost all of the choices that people, households,
businesses, and governments make. Optimization involves assessing the expected costs and benefits
and using them to make the best possible choice. Optimization can be done by looking at total value
and comparing which option is largest: A firm might consider several levels of output and choose the
one with the highest profit. However, this may not always be feasible, so optimization can also be
achieved by simply looking and marginal benefits and marginal costs: A firm should continue to
produce so long as marginal revenue is greater than marginal cost.
2. Does the principle of optimization imply that real people always choose the best feasible option?
Answer: Optimization is a good description of almost all human behavior, but this doesn’t mean that
people are always perfect calculators. Our decisions are roughly equal to the choices we would make
if we knew all relevant information and how to employ it in complicated optimization calculations.
To an economist, optimization is a good approximation of the decisions that people make.
3. Some people choose to live close to the city center; others choose to live away from the city and
take a longer commute to work every day. Does picking a location with a longer commute imply
a failure to optimize?
Answer: People will choose where to live depending on the costs and benefits of each available
alternative. For those who choose to live in an apartment away from the central business district, the
net benefit of that apartment must be higher than the net benefit from other apartments. Since costs
include the opportunity cost of time and the cost of commuting, the direct and indirect costs vary for
different people. This does not mean that they are not optimizing; they have different preferences and
face different costs. As a result, they make different decisions.
4. Why does a change in one’s opportunity cost of time imply a change in one’s optimal apartment
location?
Answer: When the opportunity cost of time is lower there is a lower cost to traveling a large distance
to get to work and social activities. Thus somebody with a lower opportunity cost of time is likely to
care less about where they live, and thus probably live farther from the places that he or she
frequently visits. On the flip side, people who value their time greatly are more likely to pay a
premium to live close to work.
5. Suppose you had information on the sales of similar homes just east and just west of the boundary
between two school districts. How could you use those data to estimate the value parents place on
the quality of their children’s schools?
Answer: Families optimize when they choose homes. Suppose schools on the west side of the school
Optimization: Doing the Best You Can
Questions
1. What is meant by optimization? Compare and contrast optimization using total value and
optimization using marginal analysis.
Answer: Optimization is the process that describes almost all of the choices that people, households,
businesses, and governments make. Optimization involves assessing the expected costs and benefits
and using them to make the best possible choice. Optimization can be done by looking at total value
and comparing which option is largest: A firm might consider several levels of output and choose the
one with the highest profit. However, this may not always be feasible, so optimization can also be
achieved by simply looking and marginal benefits and marginal costs: A firm should continue to
produce so long as marginal revenue is greater than marginal cost.
2. Does the principle of optimization imply that real people always choose the best feasible option?
Answer: Optimization is a good description of almost all human behavior, but this doesn’t mean that
people are always perfect calculators. Our decisions are roughly equal to the choices we would make
if we knew all relevant information and how to employ it in complicated optimization calculations.
To an economist, optimization is a good approximation of the decisions that people make.
3. Some people choose to live close to the city center; others choose to live away from the city and
take a longer commute to work every day. Does picking a location with a longer commute imply
a failure to optimize?
Answer: People will choose where to live depending on the costs and benefits of each available
alternative. For those who choose to live in an apartment away from the central business district, the
net benefit of that apartment must be higher than the net benefit from other apartments. Since costs
include the opportunity cost of time and the cost of commuting, the direct and indirect costs vary for
different people. This does not mean that they are not optimizing; they have different preferences and
face different costs. As a result, they make different decisions.
4. Why does a change in one’s opportunity cost of time imply a change in one’s optimal apartment
location?
Answer: When the opportunity cost of time is lower there is a lower cost to traveling a large distance
to get to work and social activities. Thus somebody with a lower opportunity cost of time is likely to
care less about where they live, and thus probably live farther from the places that he or she
frequently visits. On the flip side, people who value their time greatly are more likely to pay a
premium to live close to work.
5. Suppose you had information on the sales of similar homes just east and just west of the boundary
between two school districts. How could you use those data to estimate the value parents place on
the quality of their children’s schools?
Answer: Families optimize when they choose homes. Suppose schools on the west side of the school
Loading page 19...
Chapter 3 | Optimization: Doing the Best You Can 18
boundary are better than the schools on the east side. Families are willing to buy homes on both sides
of the boundary. This means that when families optimize they do just as well buying a home in either
school district. Therefore, the prices of homes on the east side have to be just enough lower than the
prices on the west side to persuade families to live in either district. A well-known study by Sandra
Black relied on this line of argument and found that parents were willing to pay 2.5 percent more for
a home if their children could attend schools with 5 percent higher test scores.
See Sandra E. Black “Do Better Schools Matter? Parental Valuation of Elementary Education,”
Quarterly Journal of Economics, May 1999.
6. There is a proverb “anything worth doing is worth doing well.” Do you think an economist would
agree with this proverb?
Answer: Probably not (unless this economist is one of your parents). An economist is likely to tell
you that you should follow the Principle of Optimization at the Margin and that you should do
something well only if the marginal benefits of doing it well are at least as large as the marginal costs.
Suppose you are thinking of painting your room and you have three options: decide not to paint, paint
but do a sloppy job, or paint and be meticulously careful. An economist would tell you to paint your
room carefully if the marginal benefit of being careful (i.e., the difference between how your room
would look if you are careful and how it would look if you are sloppy) is at least as large as the
additional cost of painting carefully. Remember that because of scarcity, we cannot have everything
we want. Suppose you get 95% of the benefit from painting your room to perfection while doing a
sloppy job. The additional 5% in benefits from striving for perfection may well cost more than it is
worth, in terms of alternative uses for your time.
7. Why is marginal analysis helpful for identifying the key aspects of an optimization problem?
Answer: For the sake of simplicity and intuition, economists mostly use optimization in differences,
which is called marginal analysis. For example, suppose that two apartments are both near good
restaurants, both have good access to public transportation, and both have a laundromat down the
street. The two attributes that are different, for instance rent and street noise, are compared while
ignoring all the attributes that are the same about the two apartments. When comparing two options, it
makes sense to focus on what makes them different. Marginal analysis emphasizes this point, by
comparing differences instead of levels.
8. Explain how the market for apartments allocates the scarce supply of apartments near the city
center.
Answer: The free market for apartments resolves the question of who gets to live in the best
apartments. The rental price of apartments provides incentives that effectively allocate economic
resources. As the price of downtown apartments rises, only workers with the highest opportunity cost
of time will be willing to rent them. All other workers will prefer to move further away and accept the
consequences of a longer commute.
9. Is optimization analysis positive, normative, or both? Explain your answer.
Answer: Optimization is a good positive (that is, descriptive) model of economic behavior in most,
though not all, situations. Sometimes people fail to optimize, for example, when they use average net
benefit instead of marginal net benefit to make a choice. On the other hand, optimization is always a
useful normative model. People will be better off if they are taught to optimize.
boundary are better than the schools on the east side. Families are willing to buy homes on both sides
of the boundary. This means that when families optimize they do just as well buying a home in either
school district. Therefore, the prices of homes on the east side have to be just enough lower than the
prices on the west side to persuade families to live in either district. A well-known study by Sandra
Black relied on this line of argument and found that parents were willing to pay 2.5 percent more for
a home if their children could attend schools with 5 percent higher test scores.
See Sandra E. Black “Do Better Schools Matter? Parental Valuation of Elementary Education,”
Quarterly Journal of Economics, May 1999.
6. There is a proverb “anything worth doing is worth doing well.” Do you think an economist would
agree with this proverb?
Answer: Probably not (unless this economist is one of your parents). An economist is likely to tell
you that you should follow the Principle of Optimization at the Margin and that you should do
something well only if the marginal benefits of doing it well are at least as large as the marginal costs.
Suppose you are thinking of painting your room and you have three options: decide not to paint, paint
but do a sloppy job, or paint and be meticulously careful. An economist would tell you to paint your
room carefully if the marginal benefit of being careful (i.e., the difference between how your room
would look if you are careful and how it would look if you are sloppy) is at least as large as the
additional cost of painting carefully. Remember that because of scarcity, we cannot have everything
we want. Suppose you get 95% of the benefit from painting your room to perfection while doing a
sloppy job. The additional 5% in benefits from striving for perfection may well cost more than it is
worth, in terms of alternative uses for your time.
7. Why is marginal analysis helpful for identifying the key aspects of an optimization problem?
Answer: For the sake of simplicity and intuition, economists mostly use optimization in differences,
which is called marginal analysis. For example, suppose that two apartments are both near good
restaurants, both have good access to public transportation, and both have a laundromat down the
street. The two attributes that are different, for instance rent and street noise, are compared while
ignoring all the attributes that are the same about the two apartments. When comparing two options, it
makes sense to focus on what makes them different. Marginal analysis emphasizes this point, by
comparing differences instead of levels.
8. Explain how the market for apartments allocates the scarce supply of apartments near the city
center.
Answer: The free market for apartments resolves the question of who gets to live in the best
apartments. The rental price of apartments provides incentives that effectively allocate economic
resources. As the price of downtown apartments rises, only workers with the highest opportunity cost
of time will be willing to rent them. All other workers will prefer to move further away and accept the
consequences of a longer commute.
9. Is optimization analysis positive, normative, or both? Explain your answer.
Answer: Optimization is a good positive (that is, descriptive) model of economic behavior in most,
though not all, situations. Sometimes people fail to optimize, for example, when they use average net
benefit instead of marginal net benefit to make a choice. On the other hand, optimization is always a
useful normative model. People will be better off if they are taught to optimize.
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Chapter 3 | Optimization: Doing the Best You Can 19
Problems
1. Advances in wireless communication technology reduce the non-financial costs of long commutes:
People who ride trains can get work done, and people who drive cars have more entertainment
options. If this statement is true, explain the effect on the geographic area of cities. Focus on a person
who must decide how close to live to the city center.
Answer: These advances in communication technology reduce the cost of commuting: Even though the
literal commute time may not change, people waste less of their productive time as they sit on the train or
sit in their car. The financial cost may be the same, but the non-financial costs have been reduced. This
change makes living far from the city center less costly. Therefore, all else equal, there will be upward
pressure on urban sprawl as more people are willing to make long commutes.
2. You are hired as a consultant for a local restaurant. It is considering whether to close at 9:00 p.m., or
whether to stay open an extra hour (10:00 p.m.). Based on wages and utility bills, the added cost (the
marginal cost) of staying open for each additional hour is $200.
a. If the additional revenue (the marginal revenue) during the last hour of operation is $250, what
would you recommend? By how much will profit change based on your recommendation?
b. What if the additional revenue were only $100?
c. What would you need to learn about marginal revenue for you to conclude that 9:00 p.m. is the
ideal closing time?
Answers:
a. Stay open an extra hour. If the restaurant makes this change then it will increase profit by $50 as
it will increase revenue by $250 while only incurring an additional cost of $200.
b. Close an hour earlier. Not only should the restaurant not stay open later, it should close earlier. It
will forego $100 of additional revenue, but also save $200 in additional cost. The net effect will
be an increase in profit of $100.
c. If marginal revenue is exactly (or at least close to) $200 then 9:00 is probably a good time to
close.
3. Determine whether the following statements better describe optimization using total value or
optimization using marginal analysis.
a. John is attempting to decide on a movie (all movies have the same ticket price). He determines
that the new Batman movie provides him with comparatively more of a benefit than the new
Spiderman movie and that both the Batman and Spiderman movies have comparatively more of a
benefit than the new Superman movie.
b. Marcia finds that the net benefit of flying from Chicago to Honolulu on a non-stop United
Airlines flight is $400, and the net benefit for the same trip flying on a one-stop American
Airlines flight is $200.
c. Nikki decided to jog 3 miles for exercise by reasoning that a 3-mile jog was better than either 2-
mile jog ora 4-mile jog.
d. At a yard sale, Reagan calculated that she was willing to pay $200 for a queen bed that was being
sold for $100 (generating net benefit of $100) and that she was willing to pay $220 for a king bed
that was being sold for $300 (generating net benefit of - $80).
Problems
1. Advances in wireless communication technology reduce the non-financial costs of long commutes:
People who ride trains can get work done, and people who drive cars have more entertainment
options. If this statement is true, explain the effect on the geographic area of cities. Focus on a person
who must decide how close to live to the city center.
Answer: These advances in communication technology reduce the cost of commuting: Even though the
literal commute time may not change, people waste less of their productive time as they sit on the train or
sit in their car. The financial cost may be the same, but the non-financial costs have been reduced. This
change makes living far from the city center less costly. Therefore, all else equal, there will be upward
pressure on urban sprawl as more people are willing to make long commutes.
2. You are hired as a consultant for a local restaurant. It is considering whether to close at 9:00 p.m., or
whether to stay open an extra hour (10:00 p.m.). Based on wages and utility bills, the added cost (the
marginal cost) of staying open for each additional hour is $200.
a. If the additional revenue (the marginal revenue) during the last hour of operation is $250, what
would you recommend? By how much will profit change based on your recommendation?
b. What if the additional revenue were only $100?
c. What would you need to learn about marginal revenue for you to conclude that 9:00 p.m. is the
ideal closing time?
Answers:
a. Stay open an extra hour. If the restaurant makes this change then it will increase profit by $50 as
it will increase revenue by $250 while only incurring an additional cost of $200.
b. Close an hour earlier. Not only should the restaurant not stay open later, it should close earlier. It
will forego $100 of additional revenue, but also save $200 in additional cost. The net effect will
be an increase in profit of $100.
c. If marginal revenue is exactly (or at least close to) $200 then 9:00 is probably a good time to
close.
3. Determine whether the following statements better describe optimization using total value or
optimization using marginal analysis.
a. John is attempting to decide on a movie (all movies have the same ticket price). He determines
that the new Batman movie provides him with comparatively more of a benefit than the new
Spiderman movie and that both the Batman and Spiderman movies have comparatively more of a
benefit than the new Superman movie.
b. Marcia finds that the net benefit of flying from Chicago to Honolulu on a non-stop United
Airlines flight is $400, and the net benefit for the same trip flying on a one-stop American
Airlines flight is $200.
c. Nikki decided to jog 3 miles for exercise by reasoning that a 3-mile jog was better than either 2-
mile jog ora 4-mile jog.
d. At a yard sale, Reagan calculated that she was willing to pay $200 for a queen bed that was being
sold for $100 (generating net benefit of $100) and that she was willing to pay $220 for a king bed
that was being sold for $300 (generating net benefit of - $80).
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Chapter 3 | Optimization: Doing the Best You Can 20
Answers:
a. As there are only two options this example may fall under either category, though it is closer
to optimization by marginal analysis: Notice that John never considered the overall benefit of
either move, he just considered the difference in benefits.
b. This is an example of optimization using total values. Marcia has a higher net benefit from
flying non-stop.
c. This is an example of optimization by differences since Nikki probably decided against
running a fourth mile because the costs would outweigh the benefits.
d. Reagan has evaluated her choices of yard sale beds using the total net benefit from each
option. Therefore, this is optimization using total value.
4. You are taking two courses this semester, biology and chemistry. You have quizzes coming up in
both classes. The following table shows your grade on each quiz for different numbers of hours
spent studying for each quiz. (For the purposes of this problem, assume that each hour of study
time can’t be subdivided.) For instance, the table implies that if you spent 1 hour on chemistry
and 2 hours on biology, you would get a 77 on the chemistry quiz and a 74 on the biology quiz.
Hours of Study Chemistry Biology
0 70 60
1 77 68
2 82 74
3 85 78
Your goal is to maximize your average grade on the two quizzes. Use the idea of optimization
using marginal analysis to decide how much time you should spend studying for each quiz if you
have only 1 hour in total to prepare for the two exams (in other words, you will study 1 hour for
one exam and 0 hours for the other exam). How would you allocate that single hour of study time
across the two subjects? Now repeat the analysis assuming that you have 2 hours in total to
prepare for the two exams. How would you allocate those 2 hours across the two subjects?
Finally, repeat the analysis assuming that you have 3 hours in total to prepare for the two exams.
How would you allocate those 3 hours across the two subjects?
Answer: If you had just one hour, you should study biology since you would raise your biology grade
by 68 – 60 = 8 points; if instead you studied chemistry you would raise your chemistry grade by just
77 – 70 = 7. If you had a second hour, you should study chemistry since you would raise your
chemistry grade by 77 – 70 = 7; if instead you studied biology for a second hour you would raise your
biology grade by just 74 – 68 = 6. If you had a third hour, you should study biology since you would
raise your biology grade by 74 – 68 = 6; if instead you studied chemistry you would raise your
chemistry grade by just 82 – 77 = 5.
As a check on your logic, you should see that you would have found the same answers if you had
focused on optimization in levels instead of optimization in differences. If you had just one hour to
study you would have two choices:
1. Study chemistry for one hour. Average score: (77 + 60) / 2 = 68.5
2. Study biology for one hour. Average score: (70 + 68) / 2 = 69.0
If you had two hours to study you would have three choices:
Answers:
a. As there are only two options this example may fall under either category, though it is closer
to optimization by marginal analysis: Notice that John never considered the overall benefit of
either move, he just considered the difference in benefits.
b. This is an example of optimization using total values. Marcia has a higher net benefit from
flying non-stop.
c. This is an example of optimization by differences since Nikki probably decided against
running a fourth mile because the costs would outweigh the benefits.
d. Reagan has evaluated her choices of yard sale beds using the total net benefit from each
option. Therefore, this is optimization using total value.
4. You are taking two courses this semester, biology and chemistry. You have quizzes coming up in
both classes. The following table shows your grade on each quiz for different numbers of hours
spent studying for each quiz. (For the purposes of this problem, assume that each hour of study
time can’t be subdivided.) For instance, the table implies that if you spent 1 hour on chemistry
and 2 hours on biology, you would get a 77 on the chemistry quiz and a 74 on the biology quiz.
Hours of Study Chemistry Biology
0 70 60
1 77 68
2 82 74
3 85 78
Your goal is to maximize your average grade on the two quizzes. Use the idea of optimization
using marginal analysis to decide how much time you should spend studying for each quiz if you
have only 1 hour in total to prepare for the two exams (in other words, you will study 1 hour for
one exam and 0 hours for the other exam). How would you allocate that single hour of study time
across the two subjects? Now repeat the analysis assuming that you have 2 hours in total to
prepare for the two exams. How would you allocate those 2 hours across the two subjects?
Finally, repeat the analysis assuming that you have 3 hours in total to prepare for the two exams.
How would you allocate those 3 hours across the two subjects?
Answer: If you had just one hour, you should study biology since you would raise your biology grade
by 68 – 60 = 8 points; if instead you studied chemistry you would raise your chemistry grade by just
77 – 70 = 7. If you had a second hour, you should study chemistry since you would raise your
chemistry grade by 77 – 70 = 7; if instead you studied biology for a second hour you would raise your
biology grade by just 74 – 68 = 6. If you had a third hour, you should study biology since you would
raise your biology grade by 74 – 68 = 6; if instead you studied chemistry you would raise your
chemistry grade by just 82 – 77 = 5.
As a check on your logic, you should see that you would have found the same answers if you had
focused on optimization in levels instead of optimization in differences. If you had just one hour to
study you would have two choices:
1. Study chemistry for one hour. Average score: (77 + 60) / 2 = 68.5
2. Study biology for one hour. Average score: (70 + 68) / 2 = 69.0
If you had two hours to study you would have three choices:
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Chapter 3 | Optimization: Doing the Best You Can 21
1. Study chemistry for two hours. Average score: (82 + 60) / 2 = 71.0
2. Study chemistry for one hour, study biology for one hour. Average score: (77 + 68) / 2 =
72.5
3. Study biology for two hours. Average score: (70 + 74) / 2 = 72.0
If you had three hours to study, you would have four choices:
1. Study chemistry for three hours. Average score: (85 + 60) / 2 = 72.5
2. Study chemistry for two hours, study biology for one hour. Average score: (82 + 68) / 2 =
75.0
3. Study chemistry for one hour, study biology for two hours. Average score: (77 + 74) / 2 =
75.5
4. Study biology for three hours. Average score: (70 + 78) / 2 = 74.0
5. Your total benefits from consuming different quantities of gasoline each week are shown in the
table below:
Gallons per Week Total Benefit Marginal Benefit
0 0 --
1 8
2 15
3 21
4 26
5 30
6 33
7 35
8 36
a. Complete the marginal benefit column.
b. Gasoline currently costs $4 per gallon. Use the Principle of Optimization at the Margin to find
your optimal number of gallons of gas to consume each week.
c. Some people have suggested a tax of $2 per gallon of gas as a way to reduce global warming
(burning fossil fuels such as gas releases greenhouse gases which are a major cause of rising
temperatures). Suppose the price of gas rises to $6 per gallon. Use the Principle of Optimization
at the Margin to find your optimal number of gallons of gas given this new tax on gas.
Answer:
a. The marginal benefit from consuming different quantities of gas each week are shown in the
table below:
Gallons per Week Total Benefit Marginal Benefit
0 0 --
1 8 8
2 15 7
1. Study chemistry for two hours. Average score: (82 + 60) / 2 = 71.0
2. Study chemistry for one hour, study biology for one hour. Average score: (77 + 68) / 2 =
72.5
3. Study biology for two hours. Average score: (70 + 74) / 2 = 72.0
If you had three hours to study, you would have four choices:
1. Study chemistry for three hours. Average score: (85 + 60) / 2 = 72.5
2. Study chemistry for two hours, study biology for one hour. Average score: (82 + 68) / 2 =
75.0
3. Study chemistry for one hour, study biology for two hours. Average score: (77 + 74) / 2 =
75.5
4. Study biology for three hours. Average score: (70 + 78) / 2 = 74.0
5. Your total benefits from consuming different quantities of gasoline each week are shown in the
table below:
Gallons per Week Total Benefit Marginal Benefit
0 0 --
1 8
2 15
3 21
4 26
5 30
6 33
7 35
8 36
a. Complete the marginal benefit column.
b. Gasoline currently costs $4 per gallon. Use the Principle of Optimization at the Margin to find
your optimal number of gallons of gas to consume each week.
c. Some people have suggested a tax of $2 per gallon of gas as a way to reduce global warming
(burning fossil fuels such as gas releases greenhouse gases which are a major cause of rising
temperatures). Suppose the price of gas rises to $6 per gallon. Use the Principle of Optimization
at the Margin to find your optimal number of gallons of gas given this new tax on gas.
Answer:
a. The marginal benefit from consuming different quantities of gas each week are shown in the
table below:
Gallons per Week Total Benefit Marginal Benefit
0 0 --
1 8 8
2 15 7
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Chapter 3 | Optimization: Doing the Best You Can 22
3 21 6
4 26 5
5 30 4
6 33 3
7 35 2
8 36 1
b. The price per gallon of gasoline is the same as the marginal cost per gallon for the consumer.
When the price is $4, the marginal benefit from an extra gallon is equal to the marginal cost
when 5 gallons are consumed. This is the optimal quantity of gasoline that should be
consumed each week.
c. When the marginal cost or price of gasoline increases to $6, only 3 gallons should be
consumed each week. At 3 gallons, the marginal cost equals the marginal benefit from an
extra gallon of gasoline.
6. Scott loves to go to baseball games, especially home games of the Cincinnati Reds. All else
equal, he likes to sit close to the field. He also likes to get to the stadium early to watch batting
practice. The closer he parks to the stadium the more batting practice he is able to watch (the
garages all open simultaneously). Find Scott’s optimal seat type and parking garage using the
information that follows.
Location/Seat Price Scott’s Value of
View
Diamond Seats $235 $200
Club Home $95 $130
Club Seating $85 $128
Scout Box $79 $120
Scout $69 $100
Parking location Parking Fee
(game night)
Missed Batting
Practice
Benefit of
Arrival Time
Westin parking garage $5 60 min $0
Fountain Square South Garage $10 50 min $10
West river parking $17 25 min $35
East river parking $25 10 min $50
Under Stadium parking $45 0 $60
Answer: Seat location: Scott will choose the Club Seating seats priced at $85 because this will
maximize his value from closer view. The marginal cost of the Club Home seat is $10 but his
marginal benefit is just $2, so he loses $8 by upgrading to Club Home seating. By buying Club
Seating this seat location, his total benefit rises by $10, so he should stop at this point.
Parking location and arrival time for batting practice: This decision on where to park influences
Scott’s arrival time to see batting practice. Seeing the parking location chart, we note that the closer to
the ballpark, the higher the parking fee. We also see that the closer the location of parking, the fewer
3 21 6
4 26 5
5 30 4
6 33 3
7 35 2
8 36 1
b. The price per gallon of gasoline is the same as the marginal cost per gallon for the consumer.
When the price is $4, the marginal benefit from an extra gallon is equal to the marginal cost
when 5 gallons are consumed. This is the optimal quantity of gasoline that should be
consumed each week.
c. When the marginal cost or price of gasoline increases to $6, only 3 gallons should be
consumed each week. At 3 gallons, the marginal cost equals the marginal benefit from an
extra gallon of gasoline.
6. Scott loves to go to baseball games, especially home games of the Cincinnati Reds. All else
equal, he likes to sit close to the field. He also likes to get to the stadium early to watch batting
practice. The closer he parks to the stadium the more batting practice he is able to watch (the
garages all open simultaneously). Find Scott’s optimal seat type and parking garage using the
information that follows.
Location/Seat Price Scott’s Value of
View
Diamond Seats $235 $200
Club Home $95 $130
Club Seating $85 $128
Scout Box $79 $120
Scout $69 $100
Parking location Parking Fee
(game night)
Missed Batting
Practice
Benefit of
Arrival Time
Westin parking garage $5 60 min $0
Fountain Square South Garage $10 50 min $10
West river parking $17 25 min $35
East river parking $25 10 min $50
Under Stadium parking $45 0 $60
Answer: Seat location: Scott will choose the Club Seating seats priced at $85 because this will
maximize his value from closer view. The marginal cost of the Club Home seat is $10 but his
marginal benefit is just $2, so he loses $8 by upgrading to Club Home seating. By buying Club
Seating this seat location, his total benefit rises by $10, so he should stop at this point.
Parking location and arrival time for batting practice: This decision on where to park influences
Scott’s arrival time to see batting practice. Seeing the parking location chart, we note that the closer to
the ballpark, the higher the parking fee. We also see that the closer the location of parking, the fewer
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Chapter 3 | Optimization: Doing the Best You Can 23
minutes of batting practice are missed, which increases Scott’s benefit. The marginal benefit of
parking closer to the stadium is greater than the marginal cost of parking closer for the Fountain
Square South Garage, West River Parking, and East River Parking. The marginal cost of under
stadium parking is $45 - $25 = $20 and the marginal benefit is $60 - $50 = $10. Since the marginal
cost of under stadium parking is greater than the marginal benefit Scott should choose East River
Parking.
Location/Seat Price
Scott’s marginal
cost of moving to
the next seat
Scott’s value of
closer view
Scott’s marginal
benefit of closer
view
Diamond seats $235 $140 $200 $70
Club Home $95 $10 $130 $2
Club Seating $85 $6 $128 $8
Scout Box $79 $10 $120 $20
Scout $69 X $100 X
Parking location
Parking fee
(game night)
Marginal
cost of
parking
Missed
batting
practice
Benefit of
arrival
time
Marginal
benefit of
arrival time
Westin parking
garage $5 X 60 min $0 X
Fountain Square
South Garage $10 $5 50 min $10 $10
West river parking $17 $7 25 min $35 $25
East river parking $25 $8 10 min $50 $15
Under Stadium
parking $45 $20 0 $60 $10
7. Suppose the total benefit and total cost to society of various levels of pollution reduction are as
follows:
(1)
Pollution
Reduction
(2)
Total Benefit
(3)
Total Cost
(4)
Total Net
Benefit
(5)
Marginal
Benefit
(6)
Marginal
Cost
0 0 0 -- --
1 20 9
2 38 20
3 54 33
4 68 48
5 80 65
6 90 84
a. Complete Column (4).
minutes of batting practice are missed, which increases Scott’s benefit. The marginal benefit of
parking closer to the stadium is greater than the marginal cost of parking closer for the Fountain
Square South Garage, West River Parking, and East River Parking. The marginal cost of under
stadium parking is $45 - $25 = $20 and the marginal benefit is $60 - $50 = $10. Since the marginal
cost of under stadium parking is greater than the marginal benefit Scott should choose East River
Parking.
Location/Seat Price
Scott’s marginal
cost of moving to
the next seat
Scott’s value of
closer view
Scott’s marginal
benefit of closer
view
Diamond seats $235 $140 $200 $70
Club Home $95 $10 $130 $2
Club Seating $85 $6 $128 $8
Scout Box $79 $10 $120 $20
Scout $69 X $100 X
Parking location
Parking fee
(game night)
Marginal
cost of
parking
Missed
batting
practice
Benefit of
arrival
time
Marginal
benefit of
arrival time
Westin parking
garage $5 X 60 min $0 X
Fountain Square
South Garage $10 $5 50 min $10 $10
West river parking $17 $7 25 min $35 $25
East river parking $25 $8 10 min $50 $15
Under Stadium
parking $45 $20 0 $60 $10
7. Suppose the total benefit and total cost to society of various levels of pollution reduction are as
follows:
(1)
Pollution
Reduction
(2)
Total Benefit
(3)
Total Cost
(4)
Total Net
Benefit
(5)
Marginal
Benefit
(6)
Marginal
Cost
0 0 0 -- --
1 20 9
2 38 20
3 54 33
4 68 48
5 80 65
6 90 84
a. Complete Column (4).
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Chapter 3 | Optimization: Doing the Best You Can 24
b. Use optimization in levels to show that if the US Environmental Protection Agency (EPA)
wants to maximize total net benefit, then it should require 3 units of pollution reduction.
c. Complete columns (5) and (6).
d. Show that the Principle of Optimization at the Margin would also tell the EPA to require 3
units of reduction.
Answers:
a.
(1)
Pollution
Reduction
(2)
Total
Benefit
(3)
Total Cost
(4)
Total Net
Benefit
(5)
Marginal
Benefit
(6)
Marginal
Cost
0 0 0 0
1 20 9 11
2 38 20 18
3 54 33 21
4 68 48 20
5 80 65 15
6 90 84 6
b. The highest value of Total Net Benefit in column (4) is 21. EPA achieves Total Net Benefit
of 21 by requiring 3 units of pollution reduction.
c. The table below shows the marginal benefits and costs from various levels of pollution
reduction.
(1)
Pollution
Reduction
(2)
Total
Benefit
(3)
Total Cost
(4)
Total Net
Benefit
(5)
Marginal
Benefit
(6)
Marginal
Cost
0 0 0 0 -- --
1 20 9 11 20 9
2 38 20 18 18 11
3 54 33 21 16 13
4 68 48 20 14 15
5 80 65 15 12 17
6 90 84 6 10 19
d. The Principle of Optimization at the Margin tells us that EPA should continue to increase
reduction as long as the marginal benefit from reduction is greater than the marginal cost of
reduction. The rule therefore implies that EPA should require firms to reduce the 3rd unit of
pollution (because the marginal benefit is 16 and marginal cost is 13) but not the 4th.
8. It is possible to use equations to do marginal analysis. Suppose your firm has a marginal revenue
given by MR = 10 - Q. This means that the seventh unit of output brings in 10 - 7 = $3 of
additional revenue. The marginal cost for your firm is MC = 2 + Q. This means that the seventh
unit of output increases cost by 2 + 7 = $9.
b. Use optimization in levels to show that if the US Environmental Protection Agency (EPA)
wants to maximize total net benefit, then it should require 3 units of pollution reduction.
c. Complete columns (5) and (6).
d. Show that the Principle of Optimization at the Margin would also tell the EPA to require 3
units of reduction.
Answers:
a.
(1)
Pollution
Reduction
(2)
Total
Benefit
(3)
Total Cost
(4)
Total Net
Benefit
(5)
Marginal
Benefit
(6)
Marginal
Cost
0 0 0 0
1 20 9 11
2 38 20 18
3 54 33 21
4 68 48 20
5 80 65 15
6 90 84 6
b. The highest value of Total Net Benefit in column (4) is 21. EPA achieves Total Net Benefit
of 21 by requiring 3 units of pollution reduction.
c. The table below shows the marginal benefits and costs from various levels of pollution
reduction.
(1)
Pollution
Reduction
(2)
Total
Benefit
(3)
Total Cost
(4)
Total Net
Benefit
(5)
Marginal
Benefit
(6)
Marginal
Cost
0 0 0 0 -- --
1 20 9 11 20 9
2 38 20 18 18 11
3 54 33 21 16 13
4 68 48 20 14 15
5 80 65 15 12 17
6 90 84 6 10 19
d. The Principle of Optimization at the Margin tells us that EPA should continue to increase
reduction as long as the marginal benefit from reduction is greater than the marginal cost of
reduction. The rule therefore implies that EPA should require firms to reduce the 3rd unit of
pollution (because the marginal benefit is 16 and marginal cost is 13) but not the 4th.
8. It is possible to use equations to do marginal analysis. Suppose your firm has a marginal revenue
given by MR = 10 - Q. This means that the seventh unit of output brings in 10 - 7 = $3 of
additional revenue. The marginal cost for your firm is MC = 2 + Q. This means that the seventh
unit of output increases cost by 2 + 7 = $9.
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Chapter 3 | Optimization: Doing the Best You Can 25
a. Is it a good idea to produce the seventh unit of output? Why or why not?
b. Find the Q that sets marginal cost equal to marginal revenue (MC=MR). As a preview of
upcoming chapters, try to explain why this value maximizes profit.
Answers:
a. At Q = 7 the marginal revenue is 10 - 7 = $3; the marginal cost is 2 + 7 = $10. Thus
producing a 7th unit is a terrible idea as the additional cost is much greater than the
additional benefit (revenue).
b. 10 - Q = 2 + Q implies 8 = 2*Q, thus Q = 4. At Q = 4 profits will be maximized as
marginal revenue equals marginal cost. At lower output levels, MR will exceed MR. For
instance, at Q = 3, MR = 10 – Q = 7 and MC = 2 + Q = 5, so because MR > MC the firm
definitely wants to produce the 3rd unit, and probably the 4th unit. At higher out levels,
MR will be lower than MC. For example, at Q = 5, MR = 10 – 5 = 5, while MC = 2 + 5 =
7, so the first does not want to produce a 5th unit.
a. Is it a good idea to produce the seventh unit of output? Why or why not?
b. Find the Q that sets marginal cost equal to marginal revenue (MC=MR). As a preview of
upcoming chapters, try to explain why this value maximizes profit.
Answers:
a. At Q = 7 the marginal revenue is 10 - 7 = $3; the marginal cost is 2 + 7 = $10. Thus
producing a 7th unit is a terrible idea as the additional cost is much greater than the
additional benefit (revenue).
b. 10 - Q = 2 + Q implies 8 = 2*Q, thus Q = 4. At Q = 4 profits will be maximized as
marginal revenue equals marginal cost. At lower output levels, MR will exceed MR. For
instance, at Q = 3, MR = 10 – Q = 7 and MC = 2 + Q = 5, so because MR > MC the firm
definitely wants to produce the 3rd unit, and probably the 4th unit. At higher out levels,
MR will be lower than MC. For example, at Q = 5, MR = 10 – 5 = 5, while MC = 2 + 5 =
7, so the first does not want to produce a 5th unit.
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Chapter 4
Demand, Supply, and Equilibrium
Questions
1. What is meant by holding all else equal? How is this concept used when discussing movements along
the demand curve? How is this concept used when discussing movements along the supply curve?
Answer: Holding all else equal means that everything other than the variable in question is assumed to
remain constant. When we move along a demand curve we are assuming that all of the determinants of
the demand for a good other than the price of the good (e.g., income, the prices of other goods) remain
constant. When we move along a supply curve we are assuming that all of the determinants of the supply
of a good other than the price of the good (e.g., wage rates, the price of raw material, technology) remain
constant.
2. What is meant by diminishing marginal benefits? Are you likely to experience diminishing marginal
benefits for goods that you like a lot? Are there exceptions to the general rule of diminishing marginal
benefits? (Hint: think about batteries that you would use in a flashlight that requires two batteries.)
Explain your answer.
Answer: Diminishing marginal benefit from a good suggests that the willingness to pay for an additional
unit declines as more is consumed. You are likely to experience diminishing marginal benefit even from
goods that you like a lot, although you will probably consume more of those goods before diminishing
marginal benefits sets in. The first ice cream is delicious. The second is still very tasty but not quite as
good as the first. The third might make you sick to your stomach.
Yes, there could be exceptions to the rule of diminishing marginal returns. If a flashlight does not
function without both batteries, you would experience increasing marginal benefits; the first battery is
useless but the second makes the flashlight work.
3. How is the market demand schedule derived from individual demand schedules? How does the
market demand curve differ from an individual demand curve?
Answer: We would derive the market demand schedule by summing the individual demands at every
possible price. So, for example, if Consumer 1 would buy 6 units of a good when the price is $5 and
Consumer 2 would buy 4 units, then the market demand at $5 is 10 units.
The market demand curve is the sum of the individual demand curves of all the potential buyers. The
market demand curve plots the relationship between the total quantity demanded and the market
price, holding all else equal.
4. Explain how the following factors will shift the demand curve for Gillette shaving cream.
a. The price of a competitor’s shaving cream increases.
b. With an increase in unemployment, the average level of income in the economy falls.
c. Shaving gels and foams, marketed as being better than shaving creams, are introduced in the
market.
Answer:
a. Since Gillette and other shaving creams are substitutes, an increase in the price of a competitor’s
Demand, Supply, and Equilibrium
Questions
1. What is meant by holding all else equal? How is this concept used when discussing movements along
the demand curve? How is this concept used when discussing movements along the supply curve?
Answer: Holding all else equal means that everything other than the variable in question is assumed to
remain constant. When we move along a demand curve we are assuming that all of the determinants of
the demand for a good other than the price of the good (e.g., income, the prices of other goods) remain
constant. When we move along a supply curve we are assuming that all of the determinants of the supply
of a good other than the price of the good (e.g., wage rates, the price of raw material, technology) remain
constant.
2. What is meant by diminishing marginal benefits? Are you likely to experience diminishing marginal
benefits for goods that you like a lot? Are there exceptions to the general rule of diminishing marginal
benefits? (Hint: think about batteries that you would use in a flashlight that requires two batteries.)
Explain your answer.
Answer: Diminishing marginal benefit from a good suggests that the willingness to pay for an additional
unit declines as more is consumed. You are likely to experience diminishing marginal benefit even from
goods that you like a lot, although you will probably consume more of those goods before diminishing
marginal benefits sets in. The first ice cream is delicious. The second is still very tasty but not quite as
good as the first. The third might make you sick to your stomach.
Yes, there could be exceptions to the rule of diminishing marginal returns. If a flashlight does not
function without both batteries, you would experience increasing marginal benefits; the first battery is
useless but the second makes the flashlight work.
3. How is the market demand schedule derived from individual demand schedules? How does the
market demand curve differ from an individual demand curve?
Answer: We would derive the market demand schedule by summing the individual demands at every
possible price. So, for example, if Consumer 1 would buy 6 units of a good when the price is $5 and
Consumer 2 would buy 4 units, then the market demand at $5 is 10 units.
The market demand curve is the sum of the individual demand curves of all the potential buyers. The
market demand curve plots the relationship between the total quantity demanded and the market
price, holding all else equal.
4. Explain how the following factors will shift the demand curve for Gillette shaving cream.
a. The price of a competitor’s shaving cream increases.
b. With an increase in unemployment, the average level of income in the economy falls.
c. Shaving gels and foams, marketed as being better than shaving creams, are introduced in the
market.
Answer:
a. Since Gillette and other shaving creams are substitutes, an increase in the price of a competitor’s
Loading page 28...
Chapter 4 | Demand, Supply, and Equilibrium 28
shaving cream should lead to an increase in the demand for Gillette shaving cream. This means
that the demand curve for Gillette shaving cream will shift to the right.
b. With a fall in the average income level, the demand for shaving cream is likely to fall. The
demand curve for Gillette shaving cream will shift to the left.
c. Shaving gels and foams would be considered substitutes for shaving cream. The demand curve
for Gillette shaving cream will shift to the left.
5. What does it mean to say that we are running out of “cheap oil”? What does this imply for the price of
oil in the future?
Answer: To say that we are running out of “cheap oil” means that much of the oil that is needed to meet
the demand for oil in the future is relatively expensive to find and extract. This suggests that the price of
oil will increase in the future. There is an enormous amount of oil under the surface of the earth, but for
firms to profitably drill for oil, the price of oil needs to be high enough to pay for the costs of drilling.
6. What does the Law of Supply state? What is the key feature of a typical supply curve?
Answer: The law of supply states that in most cases, the quantity supplied of a good rises when the price
of the good rises. A typical supply curve is upward sloping which shows the positive relationship between
price and quantity supplied.
7. What is the difference between willingness to accept and willingness to pay? For a trade to take place,
does the willingness to accept have to be lower, higher, or equal to the willingness to pay?
Answer: Willingness to accept is the lowest price that a seller is willing to receive to sell an extra unit of a
good, while willingness to pay is the highest price that a buyer is willing to pay for an extra unit of a
good. For a trade to take place, the buyer’s willingness to pay must be greater than or equal to the seller’s
willingness to accept.
8. Explain how the following factors will shift the supply curve for sparkling wine:
a. New irrigation technology improves the average yield of a vineyard.
b. Following an increase in the immigration of unskilled labor, the wages of wine-grape pickers fall.
c. The government sets a minimum wage for seasonal employment.
Answer:
a. With an increase in yield, the supply curve of grapes used to make sparkling wine will shift to the
right. The price of grapes will fall. Since the price of an input falls, the supply curve for sparkling
wine will shift to the right.
b. A fall in the wages of wine-grape pickers implies that the cost of producing sparkling wine has
decreased. The supply curve for sparkling wine will shift to the right.
c. A minimum wage is likely to be higher than the equilibrium wage. Since wine-grape picking is a
seasonal occupation, the wage paid to a wine-grape picker is likely to increase. This will shift the
supply curve to the left.
9. How do the following affect the equilibrium price in a market?
a. A leftward shift in demand
b. A rightward shift in supply
c. A large rightward shift in demand and a small rightward shift in supply
d. A large leftward shift in supply and a small leftward shift in demand
shaving cream should lead to an increase in the demand for Gillette shaving cream. This means
that the demand curve for Gillette shaving cream will shift to the right.
b. With a fall in the average income level, the demand for shaving cream is likely to fall. The
demand curve for Gillette shaving cream will shift to the left.
c. Shaving gels and foams would be considered substitutes for shaving cream. The demand curve
for Gillette shaving cream will shift to the left.
5. What does it mean to say that we are running out of “cheap oil”? What does this imply for the price of
oil in the future?
Answer: To say that we are running out of “cheap oil” means that much of the oil that is needed to meet
the demand for oil in the future is relatively expensive to find and extract. This suggests that the price of
oil will increase in the future. There is an enormous amount of oil under the surface of the earth, but for
firms to profitably drill for oil, the price of oil needs to be high enough to pay for the costs of drilling.
6. What does the Law of Supply state? What is the key feature of a typical supply curve?
Answer: The law of supply states that in most cases, the quantity supplied of a good rises when the price
of the good rises. A typical supply curve is upward sloping which shows the positive relationship between
price and quantity supplied.
7. What is the difference between willingness to accept and willingness to pay? For a trade to take place,
does the willingness to accept have to be lower, higher, or equal to the willingness to pay?
Answer: Willingness to accept is the lowest price that a seller is willing to receive to sell an extra unit of a
good, while willingness to pay is the highest price that a buyer is willing to pay for an extra unit of a
good. For a trade to take place, the buyer’s willingness to pay must be greater than or equal to the seller’s
willingness to accept.
8. Explain how the following factors will shift the supply curve for sparkling wine:
a. New irrigation technology improves the average yield of a vineyard.
b. Following an increase in the immigration of unskilled labor, the wages of wine-grape pickers fall.
c. The government sets a minimum wage for seasonal employment.
Answer:
a. With an increase in yield, the supply curve of grapes used to make sparkling wine will shift to the
right. The price of grapes will fall. Since the price of an input falls, the supply curve for sparkling
wine will shift to the right.
b. A fall in the wages of wine-grape pickers implies that the cost of producing sparkling wine has
decreased. The supply curve for sparkling wine will shift to the right.
c. A minimum wage is likely to be higher than the equilibrium wage. Since wine-grape picking is a
seasonal occupation, the wage paid to a wine-grape picker is likely to increase. This will shift the
supply curve to the left.
9. How do the following affect the equilibrium price in a market?
a. A leftward shift in demand
b. A rightward shift in supply
c. A large rightward shift in demand and a small rightward shift in supply
d. A large leftward shift in supply and a small leftward shift in demand
Loading page 29...
Chapter 4 | Demand, Supply, and Equilibrium 29
Answers:
a. Everything else remaining unchanged, a leftward shift in demand will lower the equilibrium price
in the market.
b. Everything else remaining unchanged, a rightward shift in supply will lower the equilibrium price
in the market.
c. Both the demand and supply curves will shift to the right but the shift in the demand curve will be
greater. This means that that equilibrium price is likely to increase.
d. Both the demand and supply curves will shift to the left but the shift in the supply curve is greater
than the shift in the demand curve. This means that the equilibrium price is likely to increase.
10. Why was a fixed price of $50 not the best way of allocating used laptops? Suggest other possible
ways of distributing the laptops that would be efficient.
Answer: At the price of $50, the quantity of laptops demanded far exceeded the quantity supplied. This
excess demand led to long queues and a stampede at the Richmond International Raceway. One of the
other ways of allocating the laptops would have been to use flexible prices. Those who valued the laptops
the most would have paid the most for them. An auction would have raised revenue and allocated the
laptops better than a fixed price. Henrico County could also have used a random lottery to allocate the
used laptops. Those who got the laptops through the lottery could have then sold it to anyone who valued
them more than they did. The lottery would not, however, lead to an efficient outcome if people who won
the lottery were not allowed to sell the laptops.
Problems
1. Suppose the following table shows the quantity of laundry detergent that is demanded and supplied at
various prices in Country 1.
P
($)
Quantity Demanded
(million oz.)
Quantity Supplied
(million oz.)
2 65 35
4 60 40
6 55 45
8 50 50
10 45 55
12 40 60
14 35 65
a. Use the data in the table to draw the demand and supply curves in the market for laundry
detergent.
b. What is the equilibrium price and quantity in the market?
c. The following tables give the demand and supply schedules for two of its neighboring countries,
Country 2 and Country 3. Suppose these three countries decide to form an economic union and
integrate their markets. Use the data in the table to plot the market demand and supply curves in
the newly formed economic union. What is the equilibrium price and quantity in the market?
Country 2:
Answers:
a. Everything else remaining unchanged, a leftward shift in demand will lower the equilibrium price
in the market.
b. Everything else remaining unchanged, a rightward shift in supply will lower the equilibrium price
in the market.
c. Both the demand and supply curves will shift to the right but the shift in the demand curve will be
greater. This means that that equilibrium price is likely to increase.
d. Both the demand and supply curves will shift to the left but the shift in the supply curve is greater
than the shift in the demand curve. This means that the equilibrium price is likely to increase.
10. Why was a fixed price of $50 not the best way of allocating used laptops? Suggest other possible
ways of distributing the laptops that would be efficient.
Answer: At the price of $50, the quantity of laptops demanded far exceeded the quantity supplied. This
excess demand led to long queues and a stampede at the Richmond International Raceway. One of the
other ways of allocating the laptops would have been to use flexible prices. Those who valued the laptops
the most would have paid the most for them. An auction would have raised revenue and allocated the
laptops better than a fixed price. Henrico County could also have used a random lottery to allocate the
used laptops. Those who got the laptops through the lottery could have then sold it to anyone who valued
them more than they did. The lottery would not, however, lead to an efficient outcome if people who won
the lottery were not allowed to sell the laptops.
Problems
1. Suppose the following table shows the quantity of laundry detergent that is demanded and supplied at
various prices in Country 1.
P
($)
Quantity Demanded
(million oz.)
Quantity Supplied
(million oz.)
2 65 35
4 60 40
6 55 45
8 50 50
10 45 55
12 40 60
14 35 65
a. Use the data in the table to draw the demand and supply curves in the market for laundry
detergent.
b. What is the equilibrium price and quantity in the market?
c. The following tables give the demand and supply schedules for two of its neighboring countries,
Country 2 and Country 3. Suppose these three countries decide to form an economic union and
integrate their markets. Use the data in the table to plot the market demand and supply curves in
the newly formed economic union. What is the equilibrium price and quantity in the market?
Country 2:
Loading page 30...
Chapter 4 | Demand, Supply, and Equilibrium 30
P ($) Quantity Demanded
(million oz.)
Quantity Supplied
(million oz.)
2 35 5
4 30 10
6 25 15
8 20 20
10 15 25
12 10 30
14 5 35
Country 3:
P ($)
Quantity Demanded
(million oz.)
Quantity Supplied
(million oz.)
2 40 10
4 35 15
6 30 20
8 25 25
10 20 30
12 15 35
14 10 40
Answers:
a. The following figure shows the domestic market for laundry detergent:
b. The equilibrium price in the market is $8 and the equilibrium quantity is 50,000,000 oz.
c. If the three countries decide to integrate, the individual country demand and supply curves need
to be aggregated to arrive at the demand and supply curves in the economic union. The following
figure shows the demand (DM) and supply (SM) curves in the economic union:
P ($) Quantity Demanded
(million oz.)
Quantity Supplied
(million oz.)
2 35 5
4 30 10
6 25 15
8 20 20
10 15 25
12 10 30
14 5 35
Country 3:
P ($)
Quantity Demanded
(million oz.)
Quantity Supplied
(million oz.)
2 40 10
4 35 15
6 30 20
8 25 25
10 20 30
12 15 35
14 10 40
Answers:
a. The following figure shows the domestic market for laundry detergent:
b. The equilibrium price in the market is $8 and the equilibrium quantity is 50,000,000 oz.
c. If the three countries decide to integrate, the individual country demand and supply curves need
to be aggregated to arrive at the demand and supply curves in the economic union. The following
figure shows the demand (DM) and supply (SM) curves in the economic union:
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